In America there is a concept of "zero tolerance" that keeps the bullied compliant and the bullies in charge. It was not until I started to get very violent that the bullying stopped. I would fight at a moments notice even sometimes in classrooms. Spent a lot of time suspended and my parents had conferences. I never lashed out at anyone. Though if someone tried to insult me, push me around, etc I would immediately switch modes and start swinging. As I got bigger and stronger it became less of an attack of weak punches to full blown knockouts.
The only way we can solve bullying is by teaching our kids that violence is not only necessary but expected. Teach them to be violent, and teach them to control it. You must defend yourself from these people. Enrolling your kids in an actual martial art (some combination of boxing, bjj, muay thai, etc) will help. When they break a bullies nose/arm/etc and get suspended you should not only encourage them to continue you should celebrate the victory. You can't win with bullies by "being the better person". Bullies aren't beat enough at home, so it's your job to bring the beatings to them. School systems are DESIGNED to protect bullies and subjugate the bullied. In America, they are prisons. The sooner children realize this the sooner they realize the methods to staying alive aren't much different.
"If you are not capable of violence you are not peaceful, you are harmless."