I had a similar problem. The version of bootstrap.js that visual studio seems to be hosed. I just pointed to this URL instead:
<link id="active_style" rel="stylesheet" href="//netdna.bootstrapcdn.com/bootswatch/3.1.1/cosmo/bootstrap.min.css">
For completeness, here's the HTML and javascript
<ul class="nav navbar-nav navbar-right">
<li id="theme_selector" class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown">Theme <b class="caret"></b></a>
<ul id="theme" class="dropdown-menu" role="menu">
<li><a href="#">Amelia</a></li>
<li><a href="#">Cerulean</a></li>
<li><a href="#">Cyborg</a></li>
<li><a href="#">Cosmo</a></li>
<li><a href="#">Darkly</a></li>
<li><a href="#">Flatly</a></li>
<li><a href="#">Lumen</a></li>
<li><a href="#">Simplex</a></li>
<li><a href="#">Slate</a></li>
<li><a href="#">Spacelab</a></li>
<li><a href="#">Superhero</a></li>
<li><a href="#">United</a></li>
<li><a href="#">Yeti</a></li>
</ul>
</li>
</ul>
Javascript
$('#theme li').click(function () {
//alert('item: ' + $(this).text());
switch_style($(this).text());
});
Hope it helps someone