http://getbootstrap.com/customize/
Above link, customizes Bootstrap's components, Less variables, and jQuery plugins to get your very own version.
I am wondering if it's possible to customize bootstrap by adding prefixes to it's classes, for example:
".container" = ".myid_container"
".btn-group" = ".myid_btn-group"
You can @extend bootstrap classes and call them whatever you want if you are using sass. Here is the info http://www.sitepoint.com/sass-semantically-extend-bootstrap/
But if you use plain bootstrap.css I'm not sure if there is a way to rename bootstrap classes except for renaming them in the file.
Just go to your bootstrap css file on any editor and then use "Find & Replace" (Ctrl + H in Notepad++) to replace all '.' with '.myid_'