About 9 days ago I was at a drive through when a car behind me rolled into my back bumper. I called the police and they arrived but the officer said we had two choices, to fill out a Form 309 or to file a police report (which would show up on the vehicle history), this is in SC. It was agreed at the scene that she would pay the cost of the repair outside of insurance. I should have had them just file a police report but in trying to be nice I think I've really screwed up.

We filled out the form 309's, she filled out her section and I filled out mine then exchanged forms. Then we both left. However we both did not exchange our insurance information and I later noticed on her form that her license plate number is not on the form. I do have her address and phone number but that is basically it.

If I do not get any payment from her outside of insurance can I still submit this accident to the insurance company to somehow get her insurance to pay for the damage? Damage came out to about $500.

Yes, if you want to, or decide to pay for the damages and not report them.