There were a couple of girls like this in dd's year in primary. DH kept saying hit her back, and I kept saying no you can't, so poor dd was very confused; I am deeply ashamed of the way I handled this situation, btw.
I saw her teacher umpteen times, face to face - we got on well - but just as when myum saw my teachers about my bully and I just got it worse next day, dd just got more targetted by her bully afterwards.
The school did try though, the girl wasn't allowed to play out at breaktimes when all the other kids, including dd, went outside, she had to go home at lunchtimes etc. But no one can keep an eye on a determined every single minute; when the girl couldn't get at dd during school day, she'd get her at the school gates and give her chinese burns, push her in bushes, taunt her, pull her hair, etc. By that time we were giving dd more independence and she was allowed to walk from school with other friends so it was a short while before she told us what was going on. The HT washed her hands of it - outside school grounds outside school time, so dh rang police.... that got the school on board again, though HT never spoke to us again or even looked at us, and dd never got the awards and things her teachers said she should have (Gifted and Talented stuff and the like). Much much worse was that after a year when they'd been in different classes, they were to be put back in the same class. We went to talk to their next year's teacher to saywe weren'thappy about it, but heinsisted that he was going to make sure they were all one happy family in hus class and they wouldn't be behaving like that; he hadn't got a clue how to stop it though. We sent dd to a different school immediately. She didn't even finish the year at the old place; it was shit.
Anyway, I think a strong push with a good loud shout is a much better idea, and I wish I'd let dh encourage her to hit back, and damn the consequences.