Busses are designed in a way in which adding seat belts would be more harmful. It has to do with a combination of the seat in front of the person, how the seat they are sitting in is made to be very strong but collapse forward where the front seat acts as an airbag of sorts.

There is a How it's Made episode on school busses that explains it in short detail.

I can say, in my area, public transportation has never had sear lets, and do not to this day. The school busses are still all very old, and I doubt they have them. They did not when i went to school, and I don't see retrofitting them without full seat replacements as they are designed to break away and assume you are not connected to the seat.