In order to get the most out of Bootstrap (especially the new "mobile first" features) I recommend using your Illustrator file as a jumping off point, rather than a spec.
I agree with the other commenter who suggested leaving the Bootstrap file in place and writing a second file with selective overrides. This is much easier with Bootstrap 3 since the flat design means less to clobber with your own declarations.
I always start with laying out a static version of the pages using plain Bootstrap then methodically cherry picking styles using the inspector (e.g. body backgrounds, typography, colors) in priority order as they stand out to me visually. I usually wind up with something that is close, but slightly different (often better), than the original design.
Good luck! If you don't fight it too hard, Bootstrap offers a lot out of the box.