Hey! Welcome to the forums! Well, given the goals you set yourself, I say you've come to the right place.
'Disarming' women always is kind of tricky; they tend to assume so much about us right off the bat... Well, actually that's a large part of the deal. Women intuitively know what you're up to. Want to hit on them? They feel it, the minute you start talking to them. Feel insecure? Doesn't go unnoticed either.
So try not to approach her with that in mind. Basically, you just want to get to know her because she seems like an interesting person. Well, your mindset seems already cool anyway, because I think just 'going for the girls' is a little shallow, and you're up to more than just that.
She still behaving weird? Just ignore it, chances are she'll start to mirror you and become more open in a matter of moments. If after all this she still is too tense, then it's time to leave. Wouldn't want a relationship with someone like that.
Also, a good opener works wonders. And by a good opener I don't mean the exact words, but the way you deliver them. I'm totally not good in this, so I'm looking at the more experienced forum members to give you some useful advice regarding this. I've turned off a potentially nice conversation by opening my mouth for the first few words and asking for the time. I've had success by just looking at her drink real funny, or offering her a chewing gum. Doing all this in the right circumstances makes all the difference. It also requires practice.
Good luck!