Asking a girl out online (facebook)

So I've met this girl at uni a few times, but one of us always seems to be going somewhere so we never have the time to talk properly for more than a few minutes. I think from our interactions that she likes me, but obviously it's difficult to tell from a few meetings.

I was thinking of adding her on facebook and then asking her out for a drink over messaging (Something like 'we keep coming across each other but never get time to talk properly - how about we grab a drink sometime?') Is this a good idea? I doubt I'll bump into her any time soon, which was why I thought I'd do this. But is it better to always ask someone out face to face?

I'd definitely try to get her number though at some point as texting is far more effective than facebook message. Do you see her often like on nights out or just during lectures and seminars?

I go to a collegiate university and see her around college (she's a fresher, I'm a second year). But I don't live in the same area as her. So I occasionally see her in college-organised events. I might have to convince my friends to go to more of them (they're lazy bastards who would rather sit around drinking and/or smoking in our rooms than meeting new people).

We do have lectures in the same building, so I could try and bump into her after that, I suppose.

I'm so depressingly inexperienced about asking girls out - my methods so far have involved getting drunk and making out with girls.