Im attracted to this girl at my gym but she always has her headphones on. Feeling s**t outta luck. Advice?

Every time I see her we smile at each other but of course with the headphones it makes it harder to actually go talk to her so I just spend the rest of the evening working out, staying in my zone and keeping to myself. As a 32 yo introverted male. One time I did go up and introduced myself and I still remember her name, but other than that, the "right time" might never come and I guess for now it just is what it is. Of course the gym isn't the place to socialize (which I know).

Updates
6 mo
Thanks for your opinions. Ill try to shoot my shot when it feels right, other than that im staying in my workout zone.
Im attracted to this girl at my gym but she always has her headphones on. Feeling s**t outta luck. Advice?
Post Opinion