This answer is for those of you looking to Install Bootstrap 3 in your Rails app without using a gem. There are two simple ways to do this that take less than 10 minutes. Pick the one that suites your needs best. Glyphicons and Javascript work and I've tested them with the latest beta of Rails 4.1.0 as well.
Using Bootstrap 3 with Rails 4 - The Bootstrap 3 files are copied into the vendor directory of your application.
Adding Bootstrap from a CDN to your Rails application - The Bootstrap 3 files are served from the Bootstrap CDN.
Number 2 above is the most flexible. All you need to do is change the version number that is stored in a layout helper. So you can run the Bootstrap version of your choice, whether that is 3.0.0, 3.0.3 or even older Bootstrap 2 releases.