Should I file a claim or pay out of pocket? How much am I looking at?

This afternoon I was backing out of my parking spot and hit the car behind me. When I finally got a hold of the girl who owned the car she seemed nice about it, but I'm worried. I took pictures of both my damage and her damage, and while I was doing so I noticed she has a large dent in her bumper BELOW where i could have possibly hit her my car merely scraped paint. When she goes to get quotes, will they make me pay for this damage as well? Is it better to just have my insurance handle it to make sure she doesn't gouge me or would it be better for me to not involve them and bite the bullet?