I'd argue that you are not liable. Although the other dog was on a leash its owner obviously did not have proper control of the dog - if she had, the other dog would not have approached your dog and your dog would not have bitten it.
Has a report been made to animal control? Has she asked for payment of any vet bills? Will your neighbor corroborate your version of the events leading to the bite?
If we do not have a signed fee agreement I am not your attorney and this is not legal advice.
That is a challenging fact-pattern. As you've described it, liability isn't clear. You could litigate it if forced, or you could attempt to arrive at a reasonably compromise to resolve the issue.
I do not practice in CA, but in WA. Here, I would advise you to wait to see how things develop. This incident could take several turns: (1) you may receive a citation for your dog biting another dog; (2) you may face administrative proceedings regarding your dog through animal control; (3) the woman could attempt to bring a civil claim against you.
Provocation is generally a key defense in these types of proceedings. You may have a provocation defense. I would consult an attorney in your area. This would give you some peace of mind and prepare you if any of these proceeding do take place.
This is not to be construed as legal advice. I do not have an attorney client relationship with you.
A roundup of the best tips and legal advice.