I doubt there was any bribery. It was common for wealthy people to get a doctor's note. There was probably an epidemic of bone spurs among young men in Trump's neighborhood during the draft years.
Did doctors write these fraudulent notes for all their patients who asked, or just the wealthy ones?
Did the draft board excuse everyone with such a fraudulent note from the physicals everyone else had to take, or just the wealthy ones?
Did anyone ever get caught?