In one school I have seen, they had problem with bullying in a class. What they did were regular meet ups of whole class with psychologist and year long programs about communication.
Kids were taught how to express what they feel (what and who makes them angry), were taught to listen to other kids, were taught to care about each others feelings, were taught what is big deal and what is not big deal.
Slowly over time, situation got better. The point is, solution was not punishment nor seeking who is guilty. It was working with all the kids, bullies, victims, bystanders and teaching them new behavioral patterns. Repeatedly saying the same things, reinforcing same values, playing similar games etc.
It is not rosy, but much better then in classes where teachers opted for punishment only or ignore it methods. There issues only grew. Yes in one case the problem kid had to leave school. Guess what - he is in another school and I don't think he magically stopped.