There are several things schools can do to lessen accidents and unwanted incidents in school.
First, it all starts with eduction. The good thing is that schools are educational institutions. So, you have already won half of the battle. For example, it is very easy to inform students in this context about the dangers of sports related injuries. A session on concussion might be a good school topic.
Second, the school should also address safety during faculty meetings. So, if school buses are operating with a certain amount of danger, then traffic patterns should be addressed. The more proactive a school is, the less reactive it will have to be.
Finally, a school could have strict rules about bullying. A zero tolerance stance might do some good. Also it is important for the school to let the parents know this as well. It is always best for the school to work with the support of parents.