You dont have to have a police report. If you call his insurance company they will give you a claims number. You tell the rep. what happened and they make a claim. They will then call the guy and if he agree's to the claim, his insurance will call you back, take an estimate and hand you a check.

I was hit in the bumper coming off a ramp going to work one day. I was a little upset, and it didnt bend the bumper, just cracked it, so he gave me his info. A month went by and I didnt hear anything, so I called his insurance company, made a claim. Got paid two days later. No police report ever involved.