Quick question about girl in my neighborhood

There is a relatively cute girl around the neighborhood. Everyone is after her though and there is no way she doesn't know about it. I have been a little distant from her and we have been invited to dinner at friends together. We didn't sit near each other and she made some comment to the point of hey, we didn't get a chance to chat to each other, that sucks. She was looking my way throughout dinner as well. Anyway, afterward I made a comment that she should have bothered to come talk to me if she wanted to chat to which I think I got a positive response. She then started fluffing and I said, as we were all walking out the house and coming down the stairs in a group, screw boring stuff, what was the most exciting thing you did this week? She didn't respond that too well and just said oh I dunno and then kinda moved back towards her friends coming down the stairs. We all walked down the street and when me and two others went our separate ways she said, oh you are going??? oh that's such a shame we didn't chat OK next time (I don't remember which one of said it but something like yeah we will have to get together to chat or something.)

Anyway to cut a long story short, I sent her an Facebook message saying hey, do you like Miles Davis? hoping she would reply what? why? or something and I would then say, well i was going to give you a chance to make it up to me for not coming over to chat the other night but you blew it with me, sorry. Anyway, she hasn't replied and she has been on Facebook since.

The last part of this story is that I am having dinner with her again on Friday... What's this girl's story, what do I do and how should I act?

A girl who goes out of her way to tell you she's sorry that you guys didn't get to chat... but doesn't respond to your FB message could be any or all of the following:

1) a player. She uses a generic line to everyone who hasn't bent backwards yet for her attentions hoping it would get him confident enough to pursue her more overtly next time. So yes, she doesn't mean it.
2) slow. She doesn't know yet how FB works and chatting her up could be the solution. Or she's still researching Miles davis and figuring out if it was a trick question
3) playing nice. Again, she doesn't really mean it but doesn't want you feeling left out or uninteresting.
4) busy. You said she is deluged by admirers. She could be online in FB and chatting up a storm with at least 10 other guys that she doesn't have the time (nor hands) to answer PMs.

Anyway, we can speculate all we want on how this girl's mind works... or you could move on to the next interesting girl. When you see her again, feel free not to mention the FB message, and let her seek you out if she really wants to. Meanwhile, you will be chatting up with interesting and interested girls.