If the two of you can't come to an agreement on the dollar amount then she is well within her right to file a claim for the damage. If you do decide to pay out of pocket I would highly recommend documenting the transaction somehow; either through a receipt, written check, or photo of the transaction. This way if she attempts to file a claim even after you have paid, you've got proof in hand that the two of you have settled on the damage. That being said, even if you don't think the amount she is asking for the repair is fair, your rate may go up even higher than that amount after a claim is filed. Our state of insurance report
(page 58) shows that an at-fault accident in California
has an average impact of $899 per year in additional premium, so that might make the decision easier.