It took 2 months for the bill to arrive.
Healthcare in US is like legal extortion. You could literally bill for breathing hospital air and people would have to pay.
Don't be ridiculous. You'd be billed for air and hospital odor separately!
Though I should note that a delivery is usually more complex than simply waiting there for the little one to fall out, there is some after care and such that is being performed plus the doctor is usually not that cheap either. (They have a lot of student debt to pay off after all)
There is also a huge industry built along the lines of phony testing.
The term used for that think is called 'basin test', basically samples are flushed down the basin and made up numbers are put in reports. You can put in what you like as the doctors know the patient is healthy.
Also, in speaking with a vascular surgeon I know, their hourly rate is between 200-350/hr. The middlemen and hospitals have figured out how to milk this cow and they're feasting.