does the gym have a website where you can find names of the staff?
maybe do an instagram search, you can filter by location and search for your gym.
i wouldn't suggest a direct approach, this shit will never work.
gyms are filled with high t males,, she probably gets hit on 20 times a day, and you would just be number 21, so really no point in trying to approach her at her workplace.
i would suggest waiting for her shift to end, then follow her, it's after work so she will probably get something to eat or will go get groceries real quick. you follow her and check out where she's going after work. you can try talking to her there, it's way better than trying the approach at her workplace.