They won't get home on this if they sue you, is my guess, so you needn't pay; you had no prior knowledge that your dog would bite, in the circumstances you were entitled to walk the dog as you did, the other owner could have kept some distance until sure of any other dog's attitude, in short they have no case on negligence or your having a dangerous dog.
If you feel morally obliged, pay the bill and mark the fact by letter saying it is paid ex gratia and without any admission of liability and the payment is to be accepted as such. If you pay it without that, they may take the payment as an admission , which you definitely don't want to happen