I tested the bootstrap dropdown menu using NVDA and they work properly, assuming they are properly tagged. You need to ensure that the element used for the dropdown "button" is a item that can take focus, it can't be a div or a span, and the ul needs to have role="menu".
To use the dropdown with NVDA for example you navigate using ↑ and ↓ and then hit enter to open the menu.
The code should look like:
<a aria-expanded="false" aria-haspopup="true" class="dropdown-toggle" data-toggle="dropdown"> Dropdown Menu Button <span class="fa fa-caret-down"> </span></a>
<ul class="dropdown-menu" role="menu">
<li><a href="https://www.google.com/" target="_blank" title="Link to Google">Link to Google</a></li>
<li>Just some Text</li>
<li><a href="http://www.stackoverlow.com/" target="_blank" title="Stack Overflow">Stack Overflow</a></li>
</ul>