Difficult one, but here's what I would do:
If like here, council libraries and leisure centres have dog poo bags which are free - collect some for them and give to them saying since they are new to the area you picked up some for them and advise where to get them. You could ask a bit about the dog at the same time, so they don't think you are unfriendly, but at least with the woman not trying to be friendly, you don't have to worry about upsetting them, it would be more difficult if you were scared of hurting their feelings. In my experience of dogs they bark because they are frightened or are protecting their territory, but most dogs like to be talked to so you could try talking to it to get it used to you without having to go as far as clapping it.