Most bullies have been bullied at home they are living what they learn and the schools and other organisations are likely to know the sad family backgrounds ... and there is enormous pressure to try and keep all children in the schools as once they fall out of education there is v little hope for them.
Unfortunately, they impact on the children who are not going thru tremendous events .... (I do appreciate there may be some children who have the best opportunities who for some reason, maybe, yet to be revealed/diagnosed psychopathic tendencies are bullies.) ... is very real and horrible to deal with.
Do you go into the school and speak to the class teacher and ask them to ensure your child is not the target of the bully and that you will be asking for updates about playtimes? This sounds like a good one?
Do you explain to your child, they have unhappy childhoods or are prob mentally ill? Potentially weaponising your child in a different way?
Do you teach your child to hit back if it carries on. Your child will likely be caught and then punished the first time this happens. Is this something you and your child are prepared for?
Two real situations.
My son in reception, had a little friend who was pushed about out of school by a neighbours child who was v large and a year younger and the little friend's dad (very lovely people) had apparently said well you must push him or hit him back.
The next day in the lunch queue my son pushed in front of his little best friend who punched him ... mortified mum and friend visiting after school. My reaction was, well it could so easily have been the other way around. All over it and remained best friends.
At first year in secondary school, older girls pushed, our girls into the road for no apparent reason when walking home. I told the school and the school intervened v sensitively and spoke to first year girls, got them to identify older girls, ensured staff on look out on way home and we parents ensured safe houses along the way home too. Never happened again.