It is usually best to call the police to the scene of any accident due to people later changing their story or promise to pay and then change their mind after they see the cost of repairs. Also police can help assign fault and an accident report is normally wanted by the insurance company.

Since the police were not called and it appears that you are trying to work this out with the at-fault driver, typically you would go and get about 3 estimates for the damages. Hopefully these estimates will all be about the same and you will show them to the at-fault party and discuss how they will pay for the repairs. At this point if the person balks at paying for the repairs you can see about placing a claim with their liability coverage or taking them to court to seek reimbursement for the cost to repair your vehicle.

As for placing a claim with your insurance company, if the expense to cost the vehicle is less than your deductible then your insurance provider would normally decline your claim since your coverage kicks in once the repair costs are over the deductible amount.

For example if your repair cost is $700 then you pay a deductible of $500 the insurance company then covers the $200 remaining. If instead your repairs cost $400 and your deductible is $500, then the expenses never reach the amount for the insurance coverage to pay out a claim so you would be better off paying the $400 for the repairs without placing a claim. This then would also not go on your claims history.

Your insurance company would not receive reimbursement for the damages or your deductible because if the deductible is more than the repair expense they would not have been out any claim money. Without placing a claim against your insurer and by not being at fault in the accident it is doubtful that your insurance premiums would be affected.

It would appear in your situation that you have the options of continuing to negotiate with the at-fault person for them to pay out of pocket to you or the repair shop for the damages. If they refuse to do so then the next option is to go through their insurance for reimbursement. The final option would be to take the person to court and try to get a judgment for the cost of fixing your vehicle.