I'd say that when she invited you up to her place late at night, and you thought she couldn't possibly have wanted to have sex with you, she probably did.
When, after each date ends, she is short and distant with you. She may be thinking that you don't like her 'that way', or don't see her as attractive, or worth being a girlfriend in a romantic sense.
If she is shy as you say, she may be waiting for you to make a move.
There is nothing wrong with a simple kiss, so when the movie is over, and you're just sitting there talking and she gives you a 'look', then kiss her!
Nature will take over from there.