Whose at fault when you have an accident on the city public trans. bus? Seat belt was not fastened and person fell out when bus stopped.

It depends on circumstances. If seatbelts were provided but not used, that would tend to put the fault on the passenger. Also, you say a person fell when the bus stopped--if it was a normal stop, or a stop to avoid some hazard (like a person suddenly walking into the street, or a car about to hit the bus), then there'd by no fault on the bus driver's or therefore bus agency's fault; the driver was doing what she was supposed to. If the stop was improper or occasioned by bad driving/driver negligence, that might establish fault and therefore liability, but would be offset by the passenger's fault in not wearing a belt.