Bullying is an offense not just against the victim but also against the school and society at large, since it disturbs the social fabric. Bullies should be required to speak over the loadspeaker and publicly and sincerely apologize to the entire school, or else face additional suspension or detention (or expulsion depending on their record). If the victim consents to it the bully may include their personal apology along with the public one. Otherwise the bully should have to deliver a separate private apology to the victim and the victim's parents.
This would make a strong statement against bullying, discouraging others from bullying and encouraging the bully to change their overall behavior for the better going into the future so other students will know that they really did change.
As much as bullies are bad and deserve to be 'punished', in no way should we publicly humiliate them. It can sound like a good idea, but in the bigger picture you are bulling them as they did you by forcing them to do something they may not feel comfortable with. I am in no way supporting the act of bulling, but there is no need to do the same to them.
It is a known fact that bullies normally have something going on at home so they try to make themselves feel better by pretending to be or trying to be better than someone else. The only way a bully should have to apologize is quietly to the victim or victims who in turn shouldn't make a big deal about it. If they have to apologize in front of the whole school then the victim will feel embarrassed and so would the bully, causing the bully to be more likely to retaliate and continue the bullying maybe even going after the same victim.
In conclusion the bully should apologize in a quiet and safe place and not in front of people that will only judge them and didn't even need to know that there was bullying going on.
Although I express sympathy for the victim, I believe more attention should be given to the bully, as they are the cause and we should fix them. Apologising in front of crowds is too much and will only result in more bullying, instead what the school could do is inform the parents and find a few reliable friends to persuade,comfort and supervise the bully as well as punishments within reason.