i think it depends on how serious the bullying is. if it's severe they should be punished and have to go to some sort of class or something. if it's teasing or something along those lines they should have to go to a class or w.e.
I think in situations where there are clear cases of bullying that the child and parent should be forced to go to some classes. Some parents are in such denial of their child's actions they need to hear it from others. I worked with a girl who was such a bully and super smurffy to everyone and when her mom was approached with clear cut evidence of her daughter's cyber bullying she didn't give a smurf and called racism.
And I also think the parents should have to as well. In my experience the majority of bullies are spoiled smurfs with smurffy parents who don't teach them the value of human life. They're the types who hate gays, hate other races, hate women etc. People like that shouldn't even be allowed to raise children imo.
I was raised in a very tolerant household and was never a big bully or anything. I think most kids do bully on some level, but with parental guidance most of them see that smurf is not okay. I was raised to respect everyone regardless of race, religion, sex/gender, weight, mental/physical abilities etc. Smurffy parents contribute greatly to smurffy kids.
I actually think punishment is generally ineffective & we do it to others so WE feel better, not so that they will change. That doesn't mean "do nothing". It means do something constructive, like classes & counseling & a lot of supervision until the child appears to be making progress & can be allowed to be trusted.