The standard advice on here, is 'just do it' and 'get more girls' (by which I guess they mean more experience at talking to girls, in the first instance at least).

there isn't a lot more we can tell you that you don't already know; the chances she would be interested lie somewhere in the region of 0-100%, and the only way to find out is to give it a go.

as a basic framework:

opener: either situational (do you know a decent place to get [coffee/clothes/whatever], or commenting on something going on around you), or direct (I like your style/shoes/top/dress/earrings). I prefer direct myself

conversation: attempt to start one once you've chatted for a bit (can be minutes), then try to move towards the idea of meeting again. keep it light and fun, this is what RSD calls calibration (reading the subtle signals/body language, gauging interest), and in my eyes is the hardest part.

close: whatever you want to get out of this (number, kiss, date, whatever).
Make it clear you find her attractive and interesting, suggest that you do something together coffee/drinks/a walk/ rock climbing/harassing homeless people (ok, probably not!), just suggest something that YOU would enjoy, don't try to cater to her interests if you don't share them.

outcome: she's either interested or not, if she is, great!
if not, have a think (now, before talking to her), is it really the end of the world? is it going to affect you in any meaningful way? as she's not even in your social circle, I can't even see how it would make anything awkward in any way. Chances are she'll at least respect the confidence you showed in asking her out.

anyway, nothing much more I can tell you, get out there and do it, and if you feel so inclined, let us know how it went.....best of luck