Not sure if I’m in the right place. Just want to see if I can get any advice on how I handled this and what I can change for future instances.

The last few months at the gym I’ve noticed this woman staring at me on multiple occasions. When I feel someone staring, I tend to look in that direction and we locked eyes on multiple occasions for 5+ seconds, but I never initiated it. Eventually, I built up the courage to wave lol. She waved back. The next two times we saw each other we waved. I built up the courage to say hello, and we introduced ourselves and spoke briefly. Spoke again the next time. Since we only crossed paths once a week(if that), I felt compelled to ask her if she would like to get some coffee because I thought there was mutual interest. When I asked, she hesitated but declined. I’m fine with it, proud of myself for putting myself out there. And if we continue to cross paths I will wave or say hello, but that’s about it. Anything I should have done differently? Did I rush it?