You’re asking two different questions here. First, the woman, and second, about prayer.
1) the woman was out of line asking you to pray with her in the first place, and she was really out of line cursing you afterwards.
2) prayer – to me, prayer is one of the most personal things that a person can do – it’s about the person’s own means of communication with the deity or spirit or whatever of his choice. In this most personal action, you (the person being asked) has the absolute right to decline. I would have said “my relationship to Cthulu (or the god of your choice) is best served by praying alone.
That said, what I say and do is dependent on who the person is who was asking. When my grandmother (z“l) was alive, she sometimes wanted me to pray with her. I did so, not out of belief, but out of respect for her and her needs. After the death of a friend of mine, his parents wanted me to pray with them while I was at their home. That’s fine, again, because it was meaningful to the parents.
But a stranger? I can’t see any reason to pray with someone I don’t know. Look at all the door-to-door evangelists (of various faiths) who want to ‘witness’ to me….