You got your CSS from CDN (bootstrapcdn.com) respond.js only works for local files. So try your website on IE8 with a local copy of bootstrap.css. Or read: CDN/X-Domain Setup
Note See also: https://github.com/scottjehl/Respond/pull/206
Update:
Please read: http://getbootstrap.com/getting-started/#support
In addition, Internet Explorer 8 requires the use of respond.js to enable media query support.
See also: https://github.com/scottjehl/Respond
For this reason the basic template contains these lines in the head section:
<!-- HTML5 shim and Respond.js IE8 support of HTML5 elements and media queries -->
<!--[if lt IE 9]>
<script src="https://stackoverflow.com/questions/17947182/assets/js/html5shiv.js"></script>
<script src="../../assets/js/respond.min.js"></script>
<![endif]-->