Auto Insurance Claims: a parking lot car accident, atm machine, collission

Question
At 2:30pm yesterday, in front of the ATM machine, I was involved n a parking lot car accident. I had been backing out of a parking space, after checking both ways to ensure no one else was backing out. I was pulling out of a parking space for a couple seconds when a 4 door sedan car began to back out her parking space without seeing me. Since I realized that, I stopped immediately and tried to honk at her, but it was too late. My car was hit by her on the right rear bumper. By now, I was the person who was farthest out when the collission occured. There was no damage on her car except a little scratch, but my bumper was messed up, the light was broken. I didn't call the police because it was just ac accident and no one was hurt. Also, the accident happened in front of the ATM. I'm wondering that the accident was recorded on the bank's camera.
My question is who I should report to, my insurance company or her insurance company. Where do I stand?

Answer
These are difficult claims to access, especially if the liability is disputed and there are no witnesses.  I would report the incident to both insurance companies as there is really no telling what the other driver will do and you don't need to have your insurance company trying to chase you down for the facts.