I'm running a BS3 based site that required support for IE8 and later. The head of your HTML structure should look something like what I have below. Note that "site.css" and "site.js" are your site-specific CSS and JavaScript library files. Tested in IE8, Firefox and Chrome:
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<meta http-equiv="X-UA-Compatible" content="IE=9; IE=8; IE=7; IE=EDGE" />
<title>PAGE TITLE HERE</title>
<!-- Load Style Sheet(s) -->
<link rel="stylesheet" type="text/css" href="Content/bootstrap.css" />
<link rel="stylesheet" type="text/css" href="Content/site.css" />
<!-- Load JavaScript(s) -->
<script src="/Scripts/jquery.js" type="text/javascript"></script>
<script src="/Scripts/bootstrap.min.js" type="text/javascript"></script>
<script src="/Scripts/respond.min.js" type="text/javascript"></script>
<script src="/Scripts/site.js" type="text/javascript"></script>
</head>