What to do if I'm at fault?

I backed into an Acura -- totally my fault -- and bashed in the front quarter panel. I told the owner I would pay for the repair, figuring I was better of handling it that way than having her file a claim with my ins co, to avoid higher rates However, the estimate from the body shop (which I trust and have used in the past) came to more than I expected -- $970. So now I'm wondering if I should tell her to file a claim instead. If it makes any difference, I've not had any claims on my policy for at least 5 years. Anyone have any thoughts?

thanks,

Eric