You have no defense what so ever.
You should have come to a complete stop. If you were rear-ended, you can come back here and talk about suing them.
And while continuing in that path while overtaking the school bus, a child could have darted out in front of that bus and you could have struck that child.I believe that if I had stopped, it would have caused more of a hazard than if I had not stopped.
I would much rather deal with suing someone for rear-ending me then defend myself in a civil lawsuit, in a courtroom with motor vehicle violations and criminal charges.
Anyway, you sound like you know better, so don't pay the fine and come back here and let us know what happens.

