Working with bootstrap in master pages has issues out of the box. This post describes how to resolve issues in your master pages.
After an extensive search for a demo that includes asp.net inside a master page, I came across a blog post at geekswithblogs.net. However, the solution to use Resolve URL did not work correctly. After some debugging, I found a post at Stack overflow using Script Manager. This finally allowed the jQuery and other scripts to work.
Please note this example uses web forms, and C#.