OP, not faulting you at all....the initial approach is always somewhat of an art...one that I am not perfect at either. As men we are use to being direct, succinct, and to the point. Where as women like a bit more ambiguity and slow soft sell, a bit of a chase. Every woman wants the beginning to feel like a fairy tale romance. So the direct approach can work, but it has to be balanced carefully.
In this girl's case, from your description she is very attractive and likely use to guys making moves on her. You are at her gym, so she didn't want to come off like a beotch and have things awkward if you bump into each other again. Which is why she gave you her number, but then let you down with the 'boyfriend' story.
More about girls.....I heard a quote once, "Make a girl's dreams come true she will love you forever." There is truth in this. Women are VERY emotoinal creatures and they live in the moment of their dreams and their emotions. Women don't follow logic...that is what we men do. The majority of female decisions and actions are emotionally driven. Girls start playing with Barbies at a young age, they dream of Ken and Barbie and babies, the big house the huge grand wedding, the loving husband and them being the princess. To have value in a girls mind, you have to be their Ken. You have to be that man that fulfills their childhood dreams. This is why the art of Projection works SOOOOO well. I love Projection and exploit it shamelessly. If you get a girl thinking about her dreams and you project yourself as that man you've won the game and hooked her.
Us guys are use to moving slow, feeling things out, weighing it with logic and also slow to commit and slow to show real intimacy / affection. But the girl that sees her dreams coming true in you, is on cloud 9. She is bragging about you to everyone and is moving at 100mph. She is not acting on logic, she is acting on her happy high emotions. Yes, to keep her hooked you might have to accelerate your pace more than you traditionally would prefer, but remember, you've become her dream man. Why would you want to do anything to shatter that?
After all, don't all of us men seek a woman who adores us, appreciates us, and wants to please us? If catering to their dreams is the cost, why not?