I have added bootstrap to my site. Here is the structure I am using. (I cannot whatsoever remove the bootstrap.css file since it I modified it to my liking).
When i use bootstrap in my rails apps i use the bootstrap-sass gem.
https://github.com/thomas-mcdonald/bootstrap-sass
You can override it. Simply import it as the docs explain. Then Import or paste your modified files.
In a php project, the glyph weren't working, i download the classic bootstrap zip and i extracted the glyph files to replace them in the project. In my memories the bug appears when you generate a custom bootstrap style from their site (the source of the bug can be wrong).
Hope this helps!