How to approach this girl at the gym?

So every Tuesday evening I tend to frequently see this girl but I can't seem to get the timing right. I go to Planet Fitness and it's a small gym. I don't want to stare at her as I'm there to focus on my workouts as much as she is. This is coming from an anxious introvert. Not only do I fear rejection but I tend to overthink and lack certain cues. If she's engrossed in her workout or something then I know that isn't a good time. Sometimes I see her sitting down what looks as if she's in-between workouts or just on her phone. That would probably be a good time to approach her from the front. All I want to say is "hey, I've seen you around here a lot and just wanted to say hi" and not be attached to the outcome. I'm also worried about how she'll react as i'm sensitive

How can I find the "right" time without overthinking it? saying "just do it" just makes it more pressuring

How to approach this girl at the gym?
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