What can I do to get my neighbor to pay for hitting my car causing over $1,000 in damage?

I backed out of my parking space about two weeks ago and was heading toward the exit of the carport area when I noticed a neighbor who parks about six carport stalls down from mine backing out of her space so I stopped allowing her plenty of room. She continued backing up in a straight line at a high speed (not sure why as she was already aligned with the exit and had plenty of room to get out) and hit the front bumper of my stopped vehicle despite my honking once I realized she wasn't going to stop. Her rear bumper has a small scratch and my front bumper and grill were damaged and cracked in several spots. After it happened, the owner of the car (who is the roommate of the person who was driving) came downstairs and told me that she would take responsibility and pay for repairs. I got a picture of her driver’s license and her phone number, but she said she didn't want to go through her insurance and would prefer to pay out-of-pocket. When I emailed her the estimate for a little over $1,000, she said the amount was too high and that she knew a “guy” who could do it for less, but I insisted on a Toyota-approved repair place since my car is only a few years old. When she finally responded by text, she said she could not afford to pay for the repairs and that she didn't think her insurance would cover the repairs, either, and asked if I could go through my insurance instead. When I called my insurance to tell them what happened, they told me they would talk to her insurance company but there isn't much they can do and that I should just pay the deductible and forget about it. I don’t think I should have to pay the $500 deductible and risk my insurance going up for something that wasn't my fault. I thought insurance companies were supposed to put more effort into getting the responsible party to pay. Why won’t her insurance cover the repairs? Because her friend was driving? If that’s the case, why can’t my insurance company go after the person who was driving?