I was in an accident with no insurance. My fault. What now?

I was in an accident yesterday, I didnt not have insurance. No police were called. Damages to both vehicles. I hydroplaned down a hill and my caliper busted, causing me to use my ebrake which did not work due to the road being wet, I made a move to wreck into the guardrail instead of traffic that was stopped at the bottom of the hill however I bounced back onto the road and rear ended the truck in front of me. Was my fault. We had no cell phone service so no police were called at the time of the accident. The driver of the other vehicle exchanged information to me but I noticed the insurance he had shown me was expired. I asked him if he had insurance and he said yes but couldnt find the card. He called me today with a ridiculous total cost of damages. While I aim to settle the matter by paying for his damages, I dont feel I should buy him a new bed for his truck when his bed suffered no damage. His bumper took damage as well as rear fender and tail light. But an entirely new bed for his truck?? I am curious to know what steps I should take. I dont know if he really has insurance or not. I think it to be smart to proceed by just assuming that he does have insurance and try to settle the matter privately but would this be a mistake? What should I do?