For starters, forget what this other dude says, maybe his game was weak or she just weren't into him.
The first interaction you had with her sounded polite and broke the ice like you said, now you need to show her that you're a man of action and you're not just going to stare or smile at her.
When you see her next and you catch her eye, finish your set then just bimble over with a nice big smile and say something like "hey I was wondering when I'd next see you" or "You know you're welcome to come spot me if you like but don't be counting if you're not going to be jumping in when i finish my set"...get and IOI out of her, make her smile and laugh but don't break her eye contact then just be direct and tell her you want to see her when she isn't all sweaty and you can have a proper conversation, ask her what time she's finishing at the gym then tell her you'll meet her out front so you can exchange numbers...
Make sure you just get on with your routine, engage with the other dudes and chicks so she can see you're a sociable person and get a bit of social proof, don't be trying to catch her eye or stare at her, just meet her outside at the time you said, try not to keep her waiting too long... Exchange numbers and tell her you'll call her the next day or the day after in the evening when you're done at the gym /work - most of the time they will say call me after 8 or just ok etc...
I can break it down even further for you if you like but i'm just here you show you the path, it's you my friend that has to walk it and decide which way you have to turn
Let us know how you play it, good luck!