Hmmm... I never thought of comparing hospitals in the same area like that before - but it does make sense. Just from looking at job postings for the places that list them online, it does seem like the more short-staffed places have bonuses more often than not.
Thankfully, I'm working with an experienced recruitment/placement firm. They'll negotiate for me whatever I ask them to, and give me feedback as to what is realistic in terms of offers. This might make it easier to keep a better distance and get perspective.
I think I will scrutinize more closely the places that have bonuses. As people have said, they must be using that bonus for a good reason. And if I can negotiate a hiring contract without a bonus, but with a higher wage, I'll at least be a free agent when I get there. Or as canoehead said, maybe I can get them to pay my moving expenses instead. A bonus would be nice, but "if it sounds too good to be true..."
Thanks everybody for the feedback!