The hospital sends their own bill. Then the doctor sends a separate bill (WTF? The doctor isn't even employed by the hospital?) The EKG tech, sonogram tech, x-ray tech, all send there own bills (often months later). Anesthesiologist, separate bill.
What exactly is the hospital bill for? Apparently, the only employee the hospital has is the billing co-ordinator, who makes sure all these separate entities know who to bill.