This looks like, bootstrap 2.3, correct? As per the documentation:
http://getbootstrap.com/2.3.2/components.html
<div class="navbar">
<div class="navbar-inner">
<div class="container">
<!-- .btn-navbar is used as the toggle for collapsed navbar content -->
<a class="btn btn-navbar" data-toggle="collapse" data-target=".nav-collapse">
<span class="icon-bar"></span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
</a>
<!-- Be sure to leave the brand out there if you want it shown -->
<a class="brand" href="#">Project name</a>
<!-- Everything you want hidden at 940px or less, place within here -->
<div class="nav-collapse collapse">
<!-- .nav, .navbar-search, .navbar-form, etc -->
</div>
</div>
</div>
The differences I see between your code and the code from the documentation is that they use an anchor tag while you're using a button, and your classes are different. Try switching those up and see if it works!