As you become more confident in yourself, develop skills to make you more attractive and learn how to talk and interact with women, you will notice that more and more women "throw themselves at you" or make the first moves.
I agree that if you are at a bar or on a date or hanging out in most situations you should kino, etc. However, this is not always possible or recommended.
I would estimate that between 70 and 80% of the girls I date make the first approach or pursue me. It never used to be this way but the more that I become a MAN, the more women find me attractive without me consciously doing anything to try and make that happen.
This girl has shown signs of liking you. Not getting a lot of time with her in a group setting and having some desperate guy monopolize her time is not going to change her feelings towards her.
The fact that you turned down one of her invitations to hang out and weren't being desperate or needy will only work in your favor.

