Your BA will probably (legally) decline to process your grievance. It may be that the investigation into the other guy that had the accident determined that he wasn't as "at fault" as was first believed. Maybe there were mitigating circumstances.
The Union's job is to stick up for the members. And there is a rule that a Teamster is not supose to harm another Teamster. So if the other guy was let off easy, the Union would consider that a GOOD thing. The Union wouldn't want you stiring up Management to start cracking down and "throwing the book" at members when they were not previously inclined to. If you were to succeed in your grievance, the Manager who agreed to go easy would look bad, become jaded, and would probably spend the rest of his career giving out the maximum punishment so as to avoid another grievance for being too leinient.
There's also something odd about bidders who drive package cars (on property or off) versus those who don't. The bidder with driving experience is penalized for his accident(s), while the bidder who has never driven has, by definition, a clean Company driving record!!!