Weird 3-week relationship. The details here are a little too scant to tell if she was hot/cold with you for no reason (e.g., a personality disorder) or if it was more the case it was just a simple summer fling for her and she never got too attached and dropped it when you did. Due to the chasing on your part, I'd sort of suspect it's more the latter... but again, not many details here, so hard to tell.
I'd have flashed her a warm smile, like what Lawliet recommends. You needn't be cold to her. It's okay if she has a man now. It's okay if she wants to act cold to you now, because she's staying loyal to her man. That's fine. If you want to pick up with her later on, just be warm, and when things end with her current guy she may circle back to you.
If you stay neutral with her, though, she's less likely to do that.
Don't chase, but do keep things warm.
I doubt the encounter had any impact on her attraction. Just a neutral encounter, where both parties were sort of surprised to see each other, but neither reacted in any way. I've had encounters like this with exes, where I was surprised to see them and just sort of blankly looked at them, and they me, and still had warm interactions with them later, and gotten back with them later (back before I adopted my current rule of "never get back with an ex").