So after watching people roll in one after the other, getting their bleeding status cleared up for free, and then just taking off to log out in a cube or idle until they're healed, I started thinking.
First I thought, "How about we make it so that if there's a registered pc doctor in the room, the NPC does nothing?", which I countered with "but what if they're AFK? Guy just bleeds out?"
Then I thought, "Okay, how about the just charges for stopping the bleeding?" Countered with, "Would a doctor really just stand there while someone was dying just because they didn't have money? He'd at least do something, right?"
Finally I got to a reasonable idea. Infections!
Whenever you're affected by the bleeding status, you have a chance of getting an infection. The chance of this is relatively high if you just walk into a clinic and let the doctor stop the bleeding before walking out. The more healing you receive (either from the NPC or a PC doctor), the less chance you have of getting an infection. Infections would be treated like any other disease (which means you'd have to go to the doctor, there'd be recovery time, and it'd be friggin expensive).
What do you guys think? Counter arguments? Expansion?