Hi K.,
I am a school bus driver and also a parent of 2 little girls myself and a 19 year old that has been there.
You are not alone in the bus bullying, many children deal with this, here is how I handle this situation on my school bus when i am aware it has gone beyond the occasional play. I speak with both children indiviually and then together and I discuss what I expect out of them both and if they don't follow these rules then its to the principals office for a nice visit and maybe a phone call to the parents where they get into more trouble. But this is just how I handle it if I am aware of it.
Now on to your driver. She told you about it, this is very pro active for her. She is aware of it going on. I would suggest to you this: Speak regularly to your bus driver, ask if she can assign the bullying child to a seat directly in the front of the bus or to make sure your daughter always has a seat in the very front of the bus so she can better watch out for her physical and mental well being. I do this alot, All the kids on my bus have assigned seats so i can better control this and i change it often. Also take this a step forward as everyone else is telling you, dont call the school, POP in for a visit with you childs principle and discuss your concerns, they get the phone message but they are so busy it takes a few days to hear back from them. Have the principle talk to the bus driver about the situation more and explain what your child is telling you and maybe not the driver, SOMETIMES we as bus drivers dont hear about anything until the parents say something to us or we hear about it from the school. When you talk to your school and the bus driver, they should contact the childs parent (they may or may not know what their child is doing to another) and they should come up with a plan to better serve your child while riding to and from school to keep her safe on all fronts.
Please always talk with your bus driver, I love when parents talk to me about their child. It helps me to better understand the child and the different situations that may happen on the school bus that I dont see because,although, I am concerned about the "picking,bullying,wrestling & hitting" on a daily basis; I am more concerned with getting your child to and from home safely and with out anyone in a vehicle hitting my bus full of GOD's most precious cargo. YES I MISS ALOT of situations that happen and NO not all the kids tell me about it. They run home and tell mom and dad. Don't count out the bus driver just yet, work with her and ask that she work with you and the school. You may be surprised to find that this same "bully" is doing it in school also and to other kids on the bus but not getting caught yet.
I hope this helps you and I am sad to hear you and all parents have this problem. It is a sign of the child growing, my own have gone through this at 9 and 6. I tell them to say to those kids who do this that they are just trying to find friends in the wrong place and to move on becasue it doesnt work to win them over to their side. SO far this seems to work and they repeat it over and over and tell when someone hits or punches them or threatens them. It wil change anyday and we will adjust our actions accordingly. I talk to them everyday about bullys because i think it very important for us as parents to always be PROACTIVE in our childs life. We are thier first line of defense and I praise you for taking this serious as most people say OH Just hit them back or something, This does not work, it makes your child a bully like the other and then you dont get to be as vocal about the other child. I hope you find this helpful in some way.