I think you're overthinking this.
I am also confused by something you said. You wrote: "unlike most attractive women at bars, she didn't play any games". But you admit to playing games ("I won't contact her for 3-4 days after we've seen each other") and you seem to want advice to get her to do what you want. You don't need to get caught up in games or other peoples' ideas of who does what when. Just be yourself. If you have a reason to call her, do it without worrying about being "needy". If you have a reason to see her, just call her up and go out without playing a waiting game.