I do not believe that bullying can or should be made into a criminal act. I think that there are already plenty of laws that could be used against bullies when they commit overt acts.
For example, if a bully is stealing from someone, they are already liable to being charged for theft. If they are physically harming the person, they can be charged with assault.
Once you go beyond things like that, the line separating criminal and non-criminal acts is too blurry for my tastes. What would constitute criminal bullying? Would it be simply making fun of other people? That would be a really tough one for a school to enforce -- when is making fun of someone bullying and when is it normal teenage behavior? It may seem easy to tell the difference, but when we start talking about how to define bullying legally, it gets pretty difficult.
I suppose it depends on how you define "criminals." I think that people that bully other people should be held accountable, but I also think that countries that use various means to bully other countries should also be held accountable.
But what I don't think is that a kid that bullies another kid in school and takes their lunch money should serve time in prison or be labeled a "criminal" for the rest of their lives.
So if you are asking if we should "criminalize" bullying, I would say no, unless of course the consequences of the bullying are equivalent to other crimes like assault or battery or murder. And in those cases, theoretically at least, those bullies are already going to be considered criminals.