So I am an international student at a US university and I have acquaintance with a German girl (of the same age but a different program) through her roommates who are my classmates. We always interact whenever we meet at their or our home for occasional dinner/drinks. We, in a group, have gone to Miami for 3 days and I think we had a good 1-hour conversation along the beach, while we were just 2 of us. I am attracted to her personality: strong mind who takes her own decisions and is inclined towards adventure-travel. So in my mind, I had noted that cool I think I like her as a person. I mostly strike the conversation with her on European ongoing politics and geography because I never had 1st experience of going there. She is mature and I am very impressed. She is cute as well. In Miami, all guys with us went for a lap dance in a strip club, but I did not feel like (could not excite me enough), so I was only chugging beer and she (my interest) got curious and asked me why am I not going? To which I replied: I am not sure if I am going to enjoy that because I am not getting excited. I possibly would be coming when I am having a heartbreak or similar things.
Now, at someone's birthday party she brought her another German friend (gorgeous than her), who told me in front of her that I am handsome (I was like wow: I come from a nationality (non-muslim) where ladies seldom compliment gents, and its mostly guys who have to take initiatives and take responsibility for most of the things and decisions). I was having kitchen conversations with her friend and her friend moved very close (she was tipsy probably and I was not drinking that day so I stepped back) and found her (my interest) passing behind and looking at me as if evaluating what I am doing with her friend.
I am not sure if she is even giving me hints, but I really would like to ask her out, even more after when her friend found me handsome meant she might be too. What I am afraid is that she may be taking me as a stereotype Indian guy. I have my hobbies (long distance running pretty positive which my Indian friends told me that I am hurting my knees that really turned me off). I dont really appreciate the demeanour of her Indian roommates mostly because when it comes to exams and assignments, they are into mass-plagiarism which is not ethically correct and I am thinking she (my interest) may be taking me as one of them as well (she is enrolled in a different program so I am assuming she doesn't know who's who much inside: we only meet her for drinks or dinners or festivals like Christmas).
What killed me more is that while I will be around in the US for at least a couple of more years, she is going back after 6 months to Germany. She would find asking her out to be practically infeasible.
I am pretty much clueless. She is a good person and I also don't want to taint good camaraderie between us.
So I would really like to know should I approach this girl or not? and if Yes, what should be my approach?
Update:
Thanks for the help guys. Well, I asked her out 2 days ago on new year's eve for going out to a nearby museum. She said "yes" in the night but next day after 16 hours, I got a text from here saying:
"I realized that it's probably not a great idea for us to go...I dont want to lead you on. You are a great guy but I am just not interested in anything at the moment. Sorry for saying yes yesterday and now saying no :("
