This mission has already failed. It's one of those things where they say you gotta jump on the opportunity when it's fresh. That first impression is the greatest. The longer you wait, the more time you've wasted for the both of you. The more time she has to think in her head, "he clearly isn't interested" and move on to other guys. Move or move on.
You're thinking too much. Find a common interest when you're chatting with her and set something up. If you're too risk adverse, you could go the sneaky way and hang out as friends, maybe with a group, but why bother? She's seen you around, knows you enough to want to hang out with you, so just ask her out. I would be a little more aggressive, but I don't know all the details. It's only awkward if you make it awkward after you ask her out, whether she says yes or no. Just remind yourself that it's more flattering than creepy, and if she thinks you're a weirdo for asking her out (highly unlikely), then she hasn't been paying much attention to you. Normally, you shouldn't poop where you eat, but at this point, it seems like she has enough vested to where you'd lose if you didn't make a move.
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Welp, Wednesday night I just did it when it seemed right and the response I got was "Was about time you asked, I was just going to give it to you myself" Ha We hung out twice already and she seems pretty awesome. Oh well, cool story bro?
Nothing really, just asked her if i can get her number to call her because we were talking about how she wanted to do something this week but didn't have any plans. So I just asked. Got it and now we hung out twice and text/talk regularly. I am going to see her again tomorrow as well.