Since you didn't mention that you were injured, I will assume that you were not. The amount of damages doesn't sound extensive, so this doesn't sound like a matter for a lawyer which means that your best recourse would be small claims court if you cannot come to a settlement.
This is an interesting fact pattern. If you were riding on the sidewalk, I would split liability 50/50. However, it appears that at the time, you were already in the driveway and no longer on the sidewalk. Her defense at that point could only be that she did not expect vehicles to come from the sidewalk. My belief is that if you were in the driveway, it's her fault for failing to see you. However, I don't think you could go wrong settling for 50%.
I dictate answers with Dragon NaturallySpeaking and sometimes I don't catch it when it occasionally types the wrong word such as probably when I mean properly. My answer is for general information purposes (a little more than entertainment) and I do not give legal advice without a personal consultation in New York. I am only licensed to practice law in the State of New York and my answer here pertains to a general question in NY.
Depending on other facts of the case, you may have less liability than you may think. If you were injured in the accident, it would be worth your while to contact an experienced bike injury attorney. I wish you the best of luck.
I would be surprised if the police consider this a hit and run since the lady stopped and identified herself. But each of you probably have a statutory duty to file a police report.
I had a very similar situation in Las Vegas. A car hit my pedestrian client in a cross walk; she took his information (but not his insurance information) and said he could go. She didn't realize how badly she was hurt. When we called him for his insurance information he said he would call back and then went silent on us.
I had my client file a police report and then I called the police and asked if they would call the driver and advise that he had an obligation to file a police report and disclose his insurance information. A detective called the driver and advised him he should call me with his insurance information. He did and I eventually settled the claim with the insurance company after filing suit.
Depending on how fast you were riding on the sidewalk and on which direction you were going, the lady who hit you may or may not have a point about it being fair to split the cost of the wheel. Of course, if you are totally not hurt, I can't imagine her ins. co. wouldn't be happy to settle for the full cost of the wheel.