FastLearner unfortunately, from what you wrote here it seems to me your in a common situation that a lot of new guys have misconceptions about. You are confusing admiration and maybe affection with attraction. The reason guys do this is they think of girls as logically reasoning guys. You said "well she invited me to dinner, so she must be interested." Well if she was a guy, absolutely. But woman do not operate like men. From what you have written about the "date" I clearly think she is either not at all interested in anything but a friendship, or may be interested but you are going to have to step up. I'm going to assume the later because the former offers no hope for you.
I will offer the fast and easy solution and the less fast , safer solution.
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plan 1. Blow me or get blown out
Ask her out again but clearly and definitely imply and explicitly set the fram as a sexual date. Say thing like
"ok lets go out for drinks here, but dress cute/sexy"
"lets see if you can do a better job kissing then that last poor effort"
"so sexy lets get together for a cocktail and what not

"
etc, make your own relevant ones up but do not hang out with her unless its under a sexual/romantic frame; not friendly frame.
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plan 2 Get on my level or I'm too busy for you
Freeze her out for a bit but then when you do talk to her tell her about all the girls you are seeing and all the crazy fun you are having whuile implying that you want to share these experiences with someone who you can care about. The point of this plan is to raise your social value while depriving her of your friendly company. Only when she has confirmed a sexual/romantic interest should you re-engage her.
These are the best two plans I know of, even still I put your chances at less then 50% because its a flubbed start. As pump says you don't want to screw up the initial framing because this is what results.