It sounds like you created a perfectly natural interaction. It may have been too much, too soon if you did more. It will be normal to be the first to say hi next time. If she is uninterested, she will barely look up, look away quick, mumble hi and focus on her task. If she is interested in people, and you, she will focus on your face, look into your eyes and say hi back in a way that you know she is willing to continue to talk.

I am 51. Boy would I be different now then I was then. Carpe Diem and all that.

What I decided sometime in my 30's, when I decided to begin a more honest life was - it is a compliment to someone if I let them know I am interested in them. Even if they are not interested back, it was still a compliment. Be honest about an interest, and respectful to being thwarted. Smile as you walk away, they said no to one of the greatest people in the world and all that.

She is interested, or she wouldn't look. Especially because she initiated the first hi. When you see her again, and you will, and she remembered you, just pause and say - Hi again, we haven't met yet, my name is ____. I have seen you around here before. Didn't you get your hair cut/fixed/changed? I really like it. (then when the uncomfortable pause begins, if she doesn't fix it - say a comfortable goodbye like). Have a great work out. Or, Gotta go, see you.

But once you open the door to talking, the door stays open til you shut it.
Remember, shyness is super sweet to girls.
Remember, this gym is a place you go for something you like, if you meet someone there, then decide you don't like them, will it be awkward? Is the gym a place you want to meet someone - so feel comfortable in the gym. It is your place. The space beneath your feet is what you own, and you are allowed to be there.

I practice feeling not awkward because I envision an MMORPG character. You know how the pixels of your character seem to exist inside a square? Well, I own the square I am in, and all the emotions I feel are allowed to live in all the space of that square, all around and beneath and above me. This is how I don't let my emotions get sucked into me like I bit a lemon and am puckering my emotions. Inflate yourself.

Being confident in myself and finding myself is basically a matter of listening to my instincts. Just listen to yourself. You are your very best friend - but we aren't always taught that. So we are upset when we don't match with what we think we should be. Then we try to change, well - who you are inside, that guy - - He is great. Just be him, and you will be very well liked.

People love confidence, and developing confidence isn't becoming someone, it is accepting the person who is already there.

Also remember, when it is natural and just flows, it is a good thing. When it is uncomfortable, and awkward, it isn't quite right. Just because at first glance you think she MIGHT be someone you want to know better - she could also be someone who you don't want to get to know better. Just because you are interested in someone at first glance, doesn't mean they will be good for YOUR soul. You have to treat others as you wish to be treated BUT you also must expect others to treat you back just as well.

Hugs, best of luck to you! (sorry if I said more then I should, I am missing my adult sons).