I find it interesting that she admitted fault, but now is being a stickler about it. Personally, if it were me, I'd be extremely happy that I didn't kill or seriously injure the cyclist, I'd live with the dent in my hood as a permanent reminder to not drive like a jacka** and pay up for the bike repairs and consider it a blessing that it didn't get reported to my insurance company. Fact of the matter is that most people do not know/appreciate the value of bikes - I used to be one of them who for the life of me couldn't even see a bike costing $250 new - yet after riding for only a few months, I saw the value in buying a $250 USED bike.

I'm glad you're ok and not having to deal with medical issues, and I can sympathize with people being a pain in the rear. Whatever you do, however, do not let it go. If nothing else, the hassle she's going through will stick with her (hopefully) and she'll be more careful while driving. Unlikely, yes, but if it happened it'd be better than if she continued driving like a jerk.

Good luck with getting the bike paid for by her. I do recommend seeing if any of your friends/relatives have a friend in the legal business who could even just write up a letter with their letterhead on it - that usually does the trick to at least scare people into taking action. She may call your bluff but from the sounds of it, you've got a pretty rock solid case (especially with the admission of fault) and so her escalating it seems unlikely.