I have had men I didn't recognize nod or wave at me in public before, or even look over my shoulder to see my phone. I always wonder if it's someone who has seen my ads, and personally it makes me feel deeply uncomfortable.

It's just not appropriate.
I know you had good intentions by doing this and her reaction was intense, but a lot could go wrong if you approach a SP in public and tell her ''I hope to see you again''...
Personally I'd be okay with a client I see often coming to say hi in public as long as he's chatting like we're friends, but not everybody feels this way. Also if I've only seen someone once or twice, it can feel invasive. I've had clients find my personal social media and try to add me on it.. There's a reason why we use aliases etc.