Should I ask a girl out on Facebook

Ok so this is what I have for all of you. I met this girl at a 3 day course i took at my school. We sat beside each other and were partners for the full 3 days. I got to know her quite well and I really do like her. Now here is the awkward part. She doesn't have a Cell Phone and I don't think her parents approve of her having a boyfriend (she is indian) so I don't have her house number either; however I am a friend of hers on Facebook. She is 17 and I am 20 years of age.
Would I come across as a douche if i emailed her via facebook about wanting to go out for a coffee or such?
I wouldn't say its a 'date' but more casual.
Any suggestions?? Tweet