Do I have to fix the bumper on a car that was not under my name and when I don't have insurance?

Similar to a question I asked yesterday...Nine months ago I "subleased" a car from my co-worker. She couldn't afford the payments on the loan anymore so I took over the payments and paid her every month for the insurance. My name was not mentioned to the bank or the insurance company at all, and my name is not on the car whatsoever. The ONLY thing we did was write up a "contract" that was not notarized, stating that I would make the car payments and pay her for insurance every month. She assured me I was covered by the insurance. (I now realize this was a stupid idea in the first place)
Well, a few months ago I damaged the front bumper and now she is trying to get me to fix it with my money. She wouldn't file a claim through the insurance, even though I've paid her for it every month, because it would jack up her insurance price. Can she take to court for this? And possibly win?

I disagree with that statement. It is slushy today (melting) and I have zero issue stopping, in both a sports car and truck. However, when it is -20 and glare ice, stopping needs to pretty much occur 1/2 block in advance

Driving speed depends on your ability to drive, tires, and vehicle. In dry ice, I usually have to do 10 k/ph under the speed limit when I don't have winter tires. Like I said, slushy/melting doesn't seem to have any effect, so I drive normally.