This might appear to be the simplest of all simple situations, but in my experience it's one that I'm haven't encountered many times. I've usually been in relationships and/or began a relationship from meeting people through friends. Recently single again, I've noticed this girl at the gym that I go to regularly and noticed she goes regularly also. I've never felt more compelled to talk to someone I don't know, but I'm not sure how to approach it without seeming weird or awkward. Here's some background so far. I've probably made eye contact with her once or twice and on occassion we work out in the same machine area. Other times, she's stretching outside a class (waiting for her friend). One time I saw her waiting outside the class and asked her if she's waiting for the next class. She said no. Then I asked if she's taken any classes before. I said which one and she said step class. I asked how that class was and she said it was good. I felt the conversation was very limited so I just bye and left sort of abruptly. It's been a few weeks since we spoke even though I've seen her there occassionally. We haven't made eye contact in close proximity so I feel it's a bit weird if I ask her how it's going if she's not even looking at me. Is there a good way to re-start a conversation with her (though, I'm not sure if she remembers me talking to her a few weeks ago)? Some situations I've though about are:

1) try to catch her working out in the same area and asking her how it's going and if she's still taking step class

2) was thinking about randomly asking her if she likes a particular sport and saying i have 2 tickets and seeing if she'd like to go. though, i'm pretty sure this sounds weird since we don't really know each other.

Do either of these sound ok or is there a better way at going about it?