I have a crush

I’ve had a crush on this girl who I see in the gym for a few months now. I’ve only seen her 7-8 times, but gosh she is beautiful. We’ve never really talked, I don’t have the courage to initiate conversation, she makes me nervous. I also think she’s already with someone, but I’m not sure. She’s never told me her name, but I know it as I’ve already used my investigative skills. I’m only going to be around this gym for another month and then I’ll probably never see her again. A part of me wants to risk it and try and ask her out/ try and talk to her. But as I said, she makes me nervous. I struggle to even keep a straight face around her. Just today I was smiling like an idiot cause I wasn’t expecting her to come to the gym, but she did. I did not know what to do with myself hahaha. What do I do?