Obviously I don't know the situation as well as you, or have all the information like you do.
I'm making a lot of assumptions out of necessity.
Here's the thing about being single: there is no requirement to go after one woman at a time. Its not an either/or with this chick. You can still maybe get something going with her in the future, while in the meantime you are getting numbers from new girls and taking them on dates.
It is perfectly okay to take more than one chick on a date in a given time frame.
And regardless of me being wrong about a few things, the fact is in this particular instance with this particular girl, you took the passive role when she invited you and you came along with what she wanted.
That's awesome that you previously took the active role and invited her on a date. She responded by not taking advantage of the opportunity you provided. This means she has low interest in you. Or at the least, it guarantees that she isn't HIGHLY INTERESTED in you. Highly interested women don't have scheduling conflicts, and if they do, they make sure to schedule a date at another time. There are no exceptions to this.
Your only currency is that you are the sole controller of her access to your time and attention. She didn't take you up on your invitation, therefore she didn't earn access to your time and attention. So don't give it to her in the future until she earns it by agreeing to your invitations.
Your willingness to take women on dates and potentially enter into a long term relationship is a big deal and it has value. So don't give it out freely. When you give it out freely, it has no value. She must earn you through her actions.
Focusing your attention on this girl is incorrect. You should instead focus on you and what you want from your interactions with women.