You want to get started with Twitter Bootstrap 3 and you want to make use of the CDN provided because it lessens the demands on your server and delivers resources fast. Everything goes well ... until you test responsive features in IE8, only to find them not working. This is simply because <IE9 does not support @media queries. However, you have included the html5shiv.js and respond.js and it still does not work!

You look at the documentation and find that you have two choices:
  1. Host the bootstrap CSS on your own server.
  2. Use a proxy, to make respond.js work cross-domain.

Some people have found alternatives to respond.js but these are regarded as slower and still need to be hosted and served.

If you are using the MaxCDN option, you do not have access to the CDN in order to upload your proxy. In short, the whole lot is rather self-defeating. You want the CDN and you want IE8 to work.

Step back a little ... respond.js attempts to reload the bootstrap CSS via AJAX, when all that is not working is the @media query in IE8. The simple solution is to serve a cut-down version of the CSS, with only the @media queries, to IE8 and below, from a local source. This is slightly inefficient because it is serving the same CSS twice but it is more efficient because it is only re-serving approx 15% of the payload. You get the best of all worlds.

Does this work? Yes, test it out here.

How do you apply it?
<link href="//maxcdn.bootstrapcdn.com/bootstrap/3.2.0/css/bootstrap.min.css" rel="stylesheet">
<!--[if lt IE 9]>
<link href="bootstrap4ie8.css" rel="stylesheet">
<script src="//oss.maxcdn.com/html5shiv/3.7.2/html5shiv.min.js"></script>
<script src="//oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
<![endif]-->

You can make your own bootstrap4ie8.css by stripping down your version of boostrap.css. You can probably optimize it further by removing parts you do not use. If you are in a hurry or just want to test this out, here is the full minimized version for boostrap 3.2.0:
@media (min-width:768px) {.lead {font-size:21px;}.dl-horizontal dt {float:left;width:160px;overflow:hidden;clear:left;text-align:right;text-overflow:ellipsis;white-space:nowrap;}.dl-horizontal dd {margin-left:180px;}.container {width:750px;}.col-sm-1, .col-sm-2, .col-sm-3, .col-sm-4, .col-sm-5, .col-sm-6, .col-sm-7, .col-sm-8, .col-sm-9, .col-sm-10, .col-sm-11, .col-sm-12 {float:left;}.col-sm-12 {width:100%;}.col-sm-11 {width:91.66666667%;}.col-sm-10 {width:83.33333333%;}.col-sm-9 {width:75%;}.col-sm-8 {width:66.66666667%;}.col-sm-7 {width:58.33333333%;}.col-sm-6 {width:50%;}.col-sm-5 {width:41.66666667%;}.col-sm-4 {width:33.33333333%;}.col-sm-3 {width:25%;}.col-sm-2 {width:16.66666667%;}.col-sm-1 {width:8.33333333%;}.col-sm-pull-12 {right:100%;}.col-sm-pull-11 {right:91.66666667%;}.col-sm-pull-10 {right:83.33333333%;}.col-sm-pull-9 {right:75%;}.col-sm-pull-8 {right:66.66666667%;}.col-sm-pull-7 {right:58.33333333%;}.col-sm-pull-6 {right:50%;}.col-sm-pull-5 {right:41.66666667%;}.col-sm-pull-4 {right:33.33333333%;}.col-sm-pull-3 {right:25%;}.col-sm-pull-2 {right:16.66666667%;}.col-sm-pull-1 {right:8.33333333%;}.col-sm-pull-0 {right:0;}.col-sm-push-12 {left:100%;}.col-sm-push-11 {left:91.66666667%;}.col-sm-push-10 {left:83.33333333%;}.col-sm-push-9 {left:75%;}.col-sm-push-8 {left:66.66666667%;}.col-sm-push-7 {left:58.33333333%;}.col-sm-push-6 {left:50%;}.col-sm-push-5 {left:41.66666667%;}.col-sm-push-4 {left:33.33333333%;}.col-sm-push-3 {left:25%;}.col-sm-push-2 {left:16.66666667%;}.col-sm-push-1 {left:8.33333333%;}.col-sm-push-0 {left:0;}.col-sm-offset-12 {margin-left:100%;}.col-sm-offset-11 {margin-left:91.66666667%;}.col-sm-offset-10 {margin-left:83.33333333%;}.col-sm-offset-9 {margin-left:75%;}.col-sm-offset-8 {margin-left:66.66666667%;}.col-sm-offset-7 {margin-left:58.33333333%;}.col-sm-offset-6 {margin-left:50%;}.col-sm-offset-5 {margin-left:41.66666667%;}.col-sm-offset-4 {margin-left:33.33333333%;}.col-sm-offset-3 {margin-left:25%;}.col-sm-offset-2 {margin-left:16.66666667%;}.col-sm-offset-1 {margin-left:8.33333333%;}.col-sm-offset-0 {margin-left:0;}.form-inline .form-group {display:inline-block;margin-bottom:0;vertical-align:middle;}.form-inline .form-control {display:inline-block;width:auto;vertical-align:middle;}.form-inline .input-group > .form-control {width:100%;}.form-inline .control-label {margin-bottom:0;vertical-align:middle;}.form-inline .radio, .form-inline .checkbox {display:inline-block;padding-left:0;margin-top:0;margin-bottom:0;vertical-align:middle;}.form-inline .radio input[type="radio"], .form-inline .checkbox input[type="checkbox"] {float:none;margin-left:0;}.form-inline .has-feedback .form-control-feedback {top:0;}.form-horizontal .control-label {text-align:right;}.navbar-right .dropdown-menu {right:0;left:auto;}.navbar-right .dropdown-menu-left {right:auto;left:0;}.nav-tabs.nav-justified > li {display:table-cell;width:1%;}.nav-tabs.nav-justified > li > a {margin-bottom:0;}.nav-tabs.nav-justified > li > a {border-bottom:1px solid #ddd;border-radius:4px 4px 0 0;}.nav-tabs.nav-justified > .active > a, .nav-tabs.nav-justified > .active > a:hover, .nav-tabs.nav-justified > .active > a:focus {border-bottom-color:#fff;}.nav-justified > li {display:table-cell;width:1%;}.nav-justified > li > a {margin-bottom:0;}.nav-tabs-justified > li > a {border-bottom:1px solid #ddd;border-radius:4px 4px 0 0;}.nav-tabs-justified > .active > a, .nav-tabs-justified > .active > a:hover, .nav-tabs-justified > .active > a:focus {border-bottom-color:#fff;}.navbar {border-radius:4px;}.navbar-header {float:left;}.navbar-collapse {width:auto;border-top:0;box-shadow:none;}.navbar-collapse.collapse {display:block !important;height:auto !important;padding-bottom:0;overflow:visible !important;}.navbar-collapse.in {overflow-y:visible;}.navbar-fixed-top .navbar-collapse, .navbar-static-top .navbar-collapse, .navbar-fixed-bottom .navbar-collapse {padding-right:0;padding-left:0;}.container > .navbar-header, .container-fluid > .navbar-header, .container > .navbar-collapse, .container-fluid > .navbar-collapse {margin-right:0;margin-left:0;}.navbar-static-top {border-radius:0;}.navbar-fixed-top, .navbar-fixed-bottom {border-radius:0;}.navbar > .container .navbar-brand, .navbar > .container-fluid .navbar-brand {margin-left:-15px;}.navbar-toggle {display:none;}.navbar-nav {float:left;margin:0;}.navbar-nav > li {float:left;}.navbar-nav > li > a {padding-top:15px;padding-bottom:15px;}.navbar-nav.navbar-right:last-child {margin-right:-15px;}.navbar-left {float:left !important;}.navbar-right {float:right !important;}.navbar-form .form-group {display:inline-block;margin-bottom:0;vertical-align:middle;}.navbar-form .form-control {display:inline-block;width:auto;vertical-align:middle;}.navbar-form .input-group > .form-control {width:100%;}.navbar-form .control-label {margin-bottom:0;vertical-align:middle;}.navbar-form .radio, .navbar-form .checkbox {display:inline-block;padding-left:0;margin-top:0;margin-bottom:0;vertical-align:middle;}.navbar-form .radio input[type="radio"], .navbar-form .checkbox input[type="checkbox"] {float:none;margin-left:0;}.navbar-form .has-feedback .form-control-feedback {top:0;}.navbar-form {width:auto;padding-top:0;padding-bottom:0;margin-right:0;margin-left:0;border:0;-webkit-box-shadow:none; box-shadow:none;}.navbar-form.navbar-right:last-child {margin-right:-15px;}.navbar-text {float:left;margin-right:15px;margin-left:15px;}.navbar-text.navbar-right:last-child {margin-right:0;}.modal-dialog {width:600px;margin:30px auto;}.modal-content {-webkit-box-shadow:0 5px 15px rgba(0, 0, 0, .5); box-shadow:0 5px 15px rgba(0, 0, 0, .5);}.modal-sm {width:300px;}.container {width:970px;}.col-md-1, .col-md-2, .col-md-3, .col-md-4, .col-md-5, .col-md-6, .col-md-7, .col-md-8, .col-md-9, .col-md-10, .col-md-11, .col-md-12 {float:left;}.col-md-12 {width:100%;}.col-md-11 {width:91.66666667%;}.col-md-10 {width:83.33333333%;}.col-md-9 {width:75%;}.col-md-8 {width:66.66666667%;}.col-md-7 {width:58.33333333%;}.col-md-6 {width:50%;}.col-md-5 {width:41.66666667%;}.col-md-4 {width:33.33333333%;}.col-md-3 {width:25%;}.col-md-2 {width:16.66666667%;}.col-md-1 {width:8.33333333%;}.col-md-pull-12 {right:100%;}.col-md-pull-11 {right:91.66666667%;}.col-md-pull-10 {right:83.33333333%;}.col-md-pull-9 {right:75%;}.col-md-pull-8 {right:66.66666667%;}.col-md-pull-7 {right:58.33333333%;}.col-md-pull-6 {right:50%;}.col-md-pull-5 {right:41.66666667%;}.col-md-pull-4 {right:33.33333333%;}.col-md-pull-3 {right:25%;}.col-md-pull-2 {right:16.66666667%;}.col-md-pull-1 {right:8.33333333%;}.col-md-pull-0 {right:0;}.col-md-push-12 {left:100%;}.col-md-push-11 {left:91.66666667%;}.col-md-push-10 {left:83.33333333%;}.col-md-push-9 {left:75%;}.col-md-push-8 {left:66.66666667%;}.col-md-push-7 {left:58.33333333%;}.col-md-push-6 {left:50%;}.col-md-push-5 {left:41.66666667%;}.col-md-push-4 {left:33.33333333%;}.col-md-push-3 {left:25%;}.col-md-push-2 {left:16.66666667%;}.col-md-push-1 {left:8.33333333%;}.col-md-push-0 {left:0;}.col-md-offset-12 {margin-left:100%;}.col-md-offset-11 {margin-left:91.66666667%;}.col-md-offset-10 {margin-left:83.33333333%;}.col-md-offset-9 {margin-left:75%;}.col-md-offset-8 {margin-left:66.66666667%;}.col-md-offset-7 {margin-left:58.33333333%;}.col-md-offset-6 {margin-left:50%;}.col-md-offset-5 {margin-left:41.66666667%;}.col-md-offset-4 {margin-left:33.33333333%;}.col-md-offset-3 {margin-left:25%;}.col-md-offset-2 {margin-left:16.66666667%;}.col-md-offset-1 {margin-left:8.33333333%;}.col-md-offset-0 {margin-left:0;}}@media (min-width:1200px) {.container {width:1170px;}.col-lg-1, .col-lg-2, .col-lg-3, .col-lg-4, .col-lg-5, .col-lg-6, .col-lg-7, .col-lg-8, .col-lg-9, .col-lg-10, .col-lg-11, .col-lg-12 {float:left;}.col-lg-12 {width:100%;}.col-lg-11 {width:91.66666667%;}.col-lg-10 {width:83.33333333%;}.col-lg-9 {width:75%;}.col-lg-8 {width:66.66666667%;}.col-lg-7 {width:58.33333333%;}.col-lg-6 {width:50%;}.col-lg-5 {width:41.66666667%;}.col-lg-4 {width:33.33333333%;}.col-lg-3 {width:25%;}.col-lg-2 {width:16.66666667%;}.col-lg-1 {width:8.33333333%;}.col-lg-pull-12 {right:100%;}.col-lg-pull-11 {right:91.66666667%;}.col-lg-pull-10 {right:83.33333333%;}.col-lg-pull-9 {right:75%;}.col-lg-pull-8 {right:66.66666667%;}.col-lg-pull-7 {right:58.33333333%;}.col-lg-pull-6 {right:50%;}.col-lg-pull-5 {right:41.66666667%;}.col-lg-pull-4 {right:33.33333333%;}.col-lg-pull-3 {right:25%;}.col-lg-pull-2 {right:16.66666667%;}.col-lg-pull-1 {right:8.33333333%;}.col-lg-pull-0 {right:0;}.col-lg-push-12 {left:100%;}.col-lg-push-11 {left:91.66666667%;}.col-lg-push-10 {left:83.33333333%;}.col-lg-push-9 {left:75%;}.col-lg-push-8 {left:66.66666667%;}.col-lg-push-7 {left:58.33333333%;}.col-lg-push-6 {left:50%;}.col-lg-push-5 {left:41.66666667%;}.col-lg-push-4 {left:33.33333333%;}.col-lg-push-3 {left:25%;}.col-lg-push-2 {left:16.66666667%;}.col-lg-push-1 {left:8.33333333%;}.col-lg-push-0 {left:0;}.col-lg-offset-12 {margin-left:100%;}.col-lg-offset-11 {margin-left:91.66666667%;}.col-lg-offset-10 {margin-left:83.33333333%;}.col-lg-offset-9 {margin-left:75%;}.col-lg-offset-8 {margin-left:66.66666667%;}.col-lg-offset-7 {margin-left:58.33333333%;}.col-lg-offset-6 {margin-left:50%;}.col-lg-offset-5 {margin-left:41.66666667%;}.col-lg-offset-4 {margin-left:33.33333333%;}.col-lg-offset-3 {margin-left:25%;}.col-lg-offset-2 {margin-left:16.66666667%;}.col-lg-offset-1 {margin-left:8.33333333%;}.col-lg-offset-0 {margin-left:0;}.visible-lg {display:block !important;}table.visible-lg {display:table;}tr.visible-lg {display:table-row !important;}th.visible-lg, td.visible-lg {display:table-cell !important;}.hidden-lg {display:none !important;}}@media (max-width:767px) {.table-responsive {width:100%;margin-bottom:15px;overflow-x:scroll;overflow-y:hidden;-webkit-overflow-scrolling:touch;-ms-overflow-style:-ms-autohiding-scrollbar;border:1px solid #ddd;}.table-responsive > .table {margin-bottom:0;}.table-responsive > .table > thead > tr > th, .table-responsive > .table > tbody > tr > th, .table-responsive > .table > tfoot > tr > th, .table-responsive > .table > thead > tr > td, .table-responsive > .table > tbody > tr > td, .table-responsive > .table > tfoot > tr > td {white-space:nowrap;}.table-responsive > .table-bordered {border:0;}.table-responsive > .table-bordered > thead > tr > th:first-child, .table-responsive > .table-bordered > tbody > tr > th:first-child, .table-responsive > .table-bordered > tfoot > tr > th:first-child, .table-responsive > .table-bordered > thead > tr > td:first-child, .table-responsive > .table-bordered > tbody > tr > td:first-child, .table-responsive > .table-bordered > tfoot > tr > td:first-child {border-left:0;}.table-responsive > .table-bordered > thead > tr > th:last-child, .table-responsive > .table-bordered > tbody > tr > th:last-child, .table-responsive > .table-bordered > tfoot > tr > th:last-child, .table-responsive > .table-bordered > thead > tr > td:last-child, .table-responsive > .table-bordered > tbody > tr > td:last-child, .table-responsive > .table-bordered > tfoot > tr > td:last-child {border-right:0;}.table-responsive > .table-bordered > tbody > tr:last-child > th, .table-responsive > .table-bordered > tfoot > tr:last-child > th, .table-responsive > .table-bordered > tbody > tr:last-child > td, .table-responsive > .table-bordered > tfoot > tr:last-child > td {border-bottom:0;}.navbar-nav .open .dropdown-menu {position:static;float:none;width:auto;margin-top:0;background-color:transparent;border:0;box-shadow:none;}.navbar-nav .open .dropdown-menu > li > a, .navbar-nav .open .dropdown-menu .dropdown-header {padding:5px 15px 5px 25px;}.navbar-nav .open .dropdown-menu > li > a {line-height:20px;}.navbar-nav .open .dropdown-menu > li > a:hover, .navbar-nav .open .dropdown-menu > li > a:focus {background-image:none;}.navbar-form .form-group {margin-bottom:5px;}.navbar-default .navbar-nav .open .dropdown-menu > li > a {color:#777;}.navbar-default .navbar-nav .open .dropdown-menu > li > a:hover, .navbar-default .navbar-nav .open .dropdown-menu > li > a:focus {color:#333;background-color:transparent;}.navbar-default .navbar-nav .open .dropdown-menu > .active > a, .navbar-default .navbar-nav .open .dropdown-menu > .active > a:hover, .navbar-default .navbar-nav .open .dropdown-menu > .active > a:focus {color:#555;background-color:#e7e7e7;}.navbar-default .navbar-nav .open .dropdown-menu > .disabled > a, .navbar-default .navbar-nav .open .dropdown-menu > .disabled > a:hover, .navbar-default .navbar-nav .open .dropdown-menu > .disabled > a:focus {color:#ccc;background-color:transparent;}.navbar-inverse .navbar-nav .open .dropdown-menu > .dropdown-header {border-color:#080808;}.navbar-inverse .navbar-nav .open .dropdown-menu .divider {background-color:#080808;}.navbar-inverse .navbar-nav .open .dropdown-menu > li > a {color:#999;}.navbar-inverse .navbar-nav .open .dropdown-menu > li > a:hover, .navbar-inverse .navbar-nav .open .dropdown-menu > li > a:focus {color:#fff;background-color:transparent;}.navbar-inverse .navbar-nav .open .dropdown-menu > .active > a, .navbar-inverse .navbar-nav .open .dropdown-menu > .active > a:hover, .navbar-inverse .navbar-nav .open .dropdown-menu > .active > a:focus {color:#fff;background-color:#080808;}.navbar-inverse .navbar-nav .open .dropdown-menu > .disabled > a, .navbar-inverse .navbar-nav .open .dropdown-menu > .disabled > a:hover, .navbar-inverse .navbar-nav .open .dropdown-menu > .disabled > a:focus {color:#444;background-color:transparent;}.visible-xs {display:block !important;}table.visible-xs {display:table;}tr.visible-xs {display:table-row !important;}th.visible-xs, td.visible-xs {display:table-cell !important;}.hidden-xs {display:none !important;}}@media screen and (min-width:768px) {.jumbotron {padding-top:48px;padding-bottom:48px;}.container .jumbotron {padding-right:60px;padding-left:60px;}.jumbotron h1, .jumbotron .h1 {font-size:63px;}.carousel-control .glyphicon-chevron-left, .carousel-control .glyphicon-chevron-right, .carousel-control .icon-prev, .carousel-control .icon-next {width:30px;height:30px;margin-top:-15px;margin-left:-15px;font-size:30px;}.carousel-caption {right:20%;left:20%;padding-bottom:30px;}.carousel-indicators {bottom:20px;}}@media (min-width:768px) and (max-width:991px) {.visible-sm {display:block !important;}table.visible-sm {display:table;}tr.visible-sm {display:table-row !important;}th.visible-sm, td.visible-sm {display:table-cell !important;}.hidden-sm {display:none !important;}}@media (min-width:992px) and (max-width:1199px) {.visible-md {display:block !important;}table.visible-md {display:table;}tr.visible-md {display:table-row !important;}th.visible-md, td.visible-md {display:table-cell !important;}.hidden-md {display:none !important;}}@media (min-width:992px) {.modal-lg {width:900px;}}@media print {* {color:#000 !important;text-shadow:none !important;background:transparent !important;box-shadow:none !important;}a, a:visited {text-decoration:underline;}a[href]:after {content:" (" attr(href) ")";}abbr[title]:after {content:" (" attr(title) ")";}a[href^="javascript:"]:after, a[href^="#"]:after {content:"";}pre, blockquote {border:1px solid #999;page-break-inside:avoid;}thead {display:table-header-group;}tr, img {page-break-inside:avoid;}img {max-width:100% !important;}p, h2, h3 {orphans:3;widows:3;}h2, h3 {page-break-after:avoid;}select {background:#fff !important;}.navbar {display:none;}.table td, .table th {background-color:#fff !important;}.btn > .caret, .dropup > .btn > .caret {border-top-color:#000 !important;}.label {border:1px solid #000;}.table {border-collapse:collapse !important;}.table-bordered th, .table-bordered td {border:1px solid #ddd !important;}.visible-print {display:block !important;}table.visible-print {display:table;}tr.visible-print {display:table-row !important;}th.visible-print, td.visible-print {display:table-cell !important;}.hidden-print {display:none !important;}}