MikeH

Answer: She didn't, she tried right away. Then Bill called her at the last minute and stopped her, out of respect for the Bride. It's only after this that we cut to four years later, when she wakes up.

Answer: Buck is wearing scrubs in the scene, so he probably works at the hospital. (A Kill Bill wiki says that he is a nurse.) Jasper is paying Buck for access and to not be disturbed while he commits the rape.

Chosen answer: Just before that, we saw her in the bathroom, oblivious to the Bride's presence, and the Bride about to get the drop on her. It's safe to assume that the blood on her mouth was a result of whatever the Bride did to her off-screen between that moment and when she presented her to O-Ren. It's hard to "try to fight back or run away" when your assailant is brandishing a katana and is literally the deadliest person in the world with that weapon. And plenty of others tried to stop the Bride...she just killed them all.