“Victim Of A Hit And Run”

just suffered a hit and run this morning, it was at a red light turning right, the person behind me bumped into my bumper. I proceeded the right turn into a near street thinking he would follow but he just took off. I got his plate number. There were very minor damages (less than 1000)to my bumper. Would the police or insurance company care about this?

Yes they absolutely would. Failing to remain at the scene of a collision is pretty serious. You should report that to both the police and your insurance company.

I do not have a dash cam on my car. How do I prove that it's him?

You don't prove anything. You report it to the police and let them deal with it.

I believe an officer will usually look up the plates for an owner and address. From there they make a visit and will ask some questions.

Radar Identified is correct. Don't be afraid to report it and let them do the rest.