You're not a terrible dog owner AT ALL. It's totally natural to feel utterly crap after an incident like this. But you clearly care deeply about your dog, as well about doing the right thing.
My dog gets nervous of big and/or intrusive dogs, and he doesn't like it when dogs greet him at the face. He'll usually let them sniff then try to get away from them. But if a dog won't leave him alone, and if I'm not able to block that dog or get the dog to move away, he will lunge/snarl/snap at the dog. No bites to date, but at the end of the day, dogs are dogs, and it does happen.
It would be ideal if everyone stopped their dogs from greeting unknown dogs without invitation, altogether. But in reality, this just doesn't happen. So as a few people have said, I'd just make a personal judgement call. A muzzle is more likely to help you relax too, which can only be a good thing in terms of the energy your doggo feels when there are other dogs around.
If it helps, I've just started muzzle training my dog too. He's always been nervous of the vet, but recently had an ear infection and tried to bite myself and the vet after being prodded for 20mins. I don't blame him, but obviously I don't want a bite situation on my hands. So now he'll wear a muzzle whenever he goes to the vet. And also in beer gardens, and on trains. Basically, anywhere he could react badly (even if he never tries to or the risk is so low). I hated the thought at first, but now I see the benefits and think it will actually be a really great thing.
I think muzzles also have the added benefit of getting people to be more conscious about staying away from a dog, so it could actually help your dog enjoy her walks more. :)
Good luck and don't beat yourself up. Things happen. Your dog hadn't done this before, and you're not a fortune teller. The other owner should have had her dogs way closer and in sight. Don't internalise her projection. She was just upset and shocked and feeling protective.