You never get anywhere in life unless you take some chances and some risks.
Based on what you've written, it sounds like she's quite interested in you......the fact that she seems so "excited" when she sees you. That's a good thing!
As for how to chill, just don't go into anything with any real expectations. Maybe organize a sort of group outing....a few of your guy friends and their girlfriends....see if she'd like to join you all, to "hang out" and then just be casual...get to really know her as a friend first.....and just see where it goes.
Sure, it might not work out, but hey...it MIGHT!