All children go through a period of being an asshole. How you handle that period of their life determines if they remain an asshole.
You want to know how to stop the bullying? Take responsibility for your little asshole. There is no way you don't know you are raising an asshole. You live with it. And I don't care how diabolical your little asshole is, he/she cannot switch it on and off. You have witnessed the asshole'ness in your home, and there is no way you think that that is reserved just for you.
You KNOW you are raising an asshole. STOP IT! If you throw your hands up and give up, it is the rest of the world that suffers.
When the bullying results in harm to another human, I think the parents of that little asshole should be made to pay. Incentive for those parents to actually 'parent' those children.
Keep it up, and when I am Queen I will make you pay.