The name of the "hospital" where Mattie wakes up is indeed Bush Hill. Bush Hill is a mansion with a terrible reputation. According to local gossip,
"Bush Hill (is) one step away from Hell, filled with dead bodies and criminals who (prey) on the weak. It (is) a place to stay away from, not a place where a young girl should lay about and sip broth..."
Bush Hill is a real place in Philadelphia, a mansion owned by Andrew Hamilton which was converted into a fever hospital during the epidemic of 1793. The hospital was run by the famed French physician Dr. Deveze, who was especially knowlegeable about the disease yellow fever.
When Mattie wakes up and discovers she is at Bush Hill, she immediately asks to leave, because of the reputation of the estate as a "dangerous place." She is assured by the attending nurse, Mrs. Flagg, that "Bush Hill is now a respectable place." Mr. Stephen Girard, a rich French merchant, importer, and banker," has taken over the establishment, getting rid of the unsavory element who has given the place its bad reputation. Mr. Girard has made Bush Hill into a place where fever victims could be taken care of under the wise and watchful eye of Dr. Deveze (Chapter 14).