It's not worth it. It's going to be too hard to prove that your cat didn't contribute to the attack or that you did correctly identify the dogs. They only have to prove that at 1%.
You can file a small claims suit in small claims court. When you go, you will be there with a bunch of other cases. The judge likely will have you go into the court's mediation room or have you try and work it out in the court room. He then will come back and begin hearing cases. If you don't have it worked out he will come to a decision based on facts and you likely will be responsible for court costs should you win or lose.
Also if you do win, the court is not going to help you collect the debt. That's up to you. You can record a judgement at an additional costs but you will have to collect that as well.
Mitigating a $500 bill in court can be more costly than it's worth. Should you lose, they can counter sue for court costs and legal fees.
What I would do is try and scare her. Fill out the appropriate paperwork and take it to her house. Tell her you are going to file a summary judgement which could entitle you to a lien on her assets if she doesn't assist you with the costs.
