I am going to be honest here - 'being busy' is THE excuse to use when you don't really want to go out with someone. It's an easy way of letting someone down without hurting their feelings. I try to be honest if i'm not interested in someone, but it's not always easy to be.
When people who I have liked have asked me out and I couldn't make the night they suggested i would say - " no i'm not free monday night but I am free wednesday". (for example)
Maybe that is just me, but i think that if she was interested then maybe she would have 'played hard to get' the first time you asked but the second time she probably would have offered an alternative day that she was free?!
I definatly wouldn't ask again, not all women may admit it or like it, but i think most prefer a little bit of a chase as well and don't always want someone to be too keen . . .
I don't want this post to sound harsh and this is just my opinion, but i am sure you would prefer to hear an honest answer :-)
I know you don't want to play games and that is good, but I bet if you acted a bit uninterested in her next time you see her (NB - don't act rude or unfriedly, just don't give her that much attention, because that is what she will be loving) and this may spark an interest from her. (she will wonder why you aren't paying her attention anymore) God that sounds so contrived but try it and see what happens . . .
If not then she just wants to be friends with you, which is what I am guessing is the case anyway.
Hope this helps
x