Bridget comes and goes on her own schedule. Mostly you don't care, except to breathe a sigh of relief when you don't have to be bothered with her--
-- but you will need her to be gone at one point, and that happens after you find your way into her hotel room.
When you've been in her room and gotten into her cell phone --
How do I get into Bridget's cell phone?
-- come down here and talk to her. You'll now have the option to tell her you saw someone going into her room; say that, and she'll be gone as long as you need to steal her dead drop.
How do I work the "dead drop" thing?