LLASY, I agree with jules. I know you say your dog is placid, and that she only takes issue with that one dog, but as you have unfortunately found out, that one grudge could lead to your dog being severely restricted or destroyed (although I hope it doesn't come to that).
I am assuming you didn't see this dog before your own dog did. If this dog lives locally, you may well have to keep your dog on a lead at all times, or take her elsewhere for her walks, as you have already begun to do.
Although your suggestions are reasonable, I don't blame the terrier's owner for refusing-from her P.O.V, it must look an awful lot like you can't control your dog, and so she probably doesn't want to put herself or her dog at risk again, especially on purpose!
Legally I am no expert, but jules' response seems about right. If you explained to the Police the measures you are taking to ensure your dog is not a danger (as this is how they will judge it-"dangerous" or "not"), you may receive a verbal warning with conditions.
In terms of parting with your cash, do you get a receipt from either this woman, or from the Vets' if paying directly? It's just worth considering, because if there's no evidence of payment, she could easily say you haven't contributed.