In my experience, the bully has already succeeded in doing a lot of damage before there is any intervention. Some comments here are the equivalent (lehavdil alfei havdalos) of expecting to negotiate with a terrorist. Bullies know exactly how to respond to all these peaches and cream speeches. They shake their heads, they agree to all the admonitions, they look for ways to incriminate the victim, and they then do whatever they please. Ask any victim. The ZERO TOLERANCE idea means that strong ACTION needs to be taken. Aside from professional evaluation and intervention for the bully, there must be exposure to the class that there is bullying occurring, and that action is being taken. If that costs the rodef his/her place in the class, that may be a last resort, but one that the school is ready to take. Once safety has been regained for the class, all the lessons about midos, bein odom lachaveiro, social skills, etc. can be taught.
I find it offensive to read the generalizations about the home lives of the bullies. Neither the bully nor the victim is being abused at home – as a deduction from the bullying observed in the school setting. Kids just have certain tendencies. Blaming on parents is foolish. That does not mean that all home lives are without flaws. But school bullying does not necessarily reflect on the home. It is unfair to make this judgment.