You can totally go to a bar even though you don't drink - people are selfabsorbed (which isn't a bad thing) and aren't paying much attention to anyone besides themselves and perhaps the other gender they are trying to get lucky with
You can always ask for a glass of water and say that it's a straight vodka, or just tell the truth and say that it's water. If the girl isn't fine with it - then it's not a woman you would want to be with for the long run. But then again, I'm assuming you can order water in a bar, seeing as I'm not a night life man myself.
But in all honesty, I recommend trying to get more self confident - that is a biggie. That is actually the best thing you can do for yourself, because it's really nerve wrecking talking to a stranger, and - unless you do it every single day - you have to have quite a bit of self confidence when you see a women giving you the green light (sadly I don't have much of it, but if I see a girl giving me the green light to talk to her then I try to pump a little inside of me ...oooeeerrrr)
And that's my next point - learning to identify the flirting signals women give out. Then you can approach them everywhere.
I don't approach everyday, frankly I don't do it very often and only in my college environment, and I've had three kinds of experiences so far; the girls that light up like christmas trees when you speak to them (that is very rewarding in it self; those girls I had been observing for a while and they were always giving me the green light to appraoch them for a long time); the second one can be best described as the "deer in headlights look" when they don't believe that you are talking to them (again, those are girls that I had been noticing their signals for quite a while). And my third observation is in regards to only one girl - she got so nervous when I approached her that she only gave me one-worded answers; I hadn't seen her before but she gave me very strongs signals to approach her (she even had her female friend walking behind her when they two walked in front of me (I was seated) just to see if I was paying attention to her); I had to go to the bathroom and pump myself up in front of the mirror to try to get some courage to approach her, so maybe I came on too strong when I approached her, but she was nervous.
The fourth response is that girls will walk away. That I saw on a "pua" youtube-video; I've never approached a girl in the street, but that is one behaviour that one can and should expect.
I'm listing these four down for you as I've done some studying on how to approach girls, and not one of the literature has tried to describe what to expect in the first few seconds - except for that YouTube video.
But I highly recommend learning about female flirting signals; bound to be loads of reading material online. I actually read a book about that, which I highly recommend and can send you the title of in a pm; don't know if there's an ebook version on torrentz but there probably is if you want it for free.