Well, good to see ignorance is still alive and well when it comes to isurance claims. Do you see me offering medical advice? No, because I am not a doctor. But that doesn't stop many of you from offering advice on insurance claims, even though you have no idea what's going on.
Comparative liability is a sticky issue. They have determined that you (the cyclist)should have been able to avoid this loss. By law, they should have put this in writing, along with their reasoning. Your job at this point, since you are not represented, is to prove that they are wrong. You said she was making a left? Which direction were you travelling, and which direction was she facing? Did she have a stop sign? How far away were you when you saw her? Did she have her indicator on? Provide the facts, and I am happy to help you draft a letter. The fact that she stopped actually helps your claim. Where did you impact her vehicle? Has she given a statement? Ask if you can get a copy of it. She'll say she didn't see you at all, or didn't see you until she pulled out. You'll want to know what it was that made her notice you.
You don't need a lawyer, unless you are injured. You won't find one to take on your damage claim. You don't need to send her any letters, as she's required to forward them to her carrier anyway. Taking her to small claims court will be a waste of time until you can establish liability 100% on her. Any injury claim you make is completely separate from a damage claim, and they cannot tie them together in any way. They're going to want 40% of her damages - legally they still need to pay you the 60%, they cannot withhold it if you refuse to pay her damages.
I'm happy to help in any way I can. You can post here or PM me. As I stated already, because you have no insurance, it will be up to you to prove that you have no liability here. That is the only thing that will change the outcome of this. To everyone that thinks insurance companies are all out to rip you off, pull your head out. You don't have all the facts. As I read it so far, they're certainly within their rights to put some liability on the cyclist. Now we just need to prove them wrong.
Cheers.