Time to introduce yourself. If her fourth and fifth words to you include, "my boyfriend," you have your answer. If they don't, proceed (with caution, of course). lol
Say "hello" and see where it goes from there?
I like the asking her to spot you approach...
You are way over thinking it. You want her to like you. Just be yourself. The best advice I have ever received about being likable was to stop trying to be interesting and start being interested.
Tell her you are a wet shaver!
My only suggestion would be to remove the shave cream from your eyebrows and face before you do anything. Good luck.
Smile be friendly ask how's it going. If she smiles back and gets chatty she's interested. If she forces a smile and says good she's not.
Also, how did you meet your wife or partner? Do they have anything to say about my problem at the gym?
Perhaps hide in her locker. When she goes to get changed and opens her locker introduce yourself.
I met my wife in a bar on New Years Eve, while wearing a purple cardboard fez. If you approach her without wearing a piece of novelty headgear you've already got more game then me.
Go get her Tiger.