You probably need to accept that there'll be a few reactions such as 'is she going to judge me for drinking' and 'is asking why going to make things a bit awkward' when you tell people you don't drink. But once you've addressed those it should be pretty easy for people to just accept it.
I mean some of my best friends are tee-total, they're great to hang out with and although I don't drink in their presence it's only because I usually just drink socially anyway, and not that much at that. I'd choose hanging out with them without drinking over going out with a bunch of people I don't know so well any day.
It's really not a big deal so I don't see why it should be with regards to dating someone either.

I wouldn't WANT to be with someone who cared if I didn't drink. I don't care if you drink, so why do you care if I don't?? If someone judges you for not drinking then they're not worth your time, in my opinion. I've ditched several guys because they gave me a hard time about not drinking. It's none of their business!

I wouldn't mind it...but would think she would be really, really thirsty after a while.

Seriously, it's no big deal. My ex didn't drink at all, and I only drank slightly. He was happy to be the designated driver for all of his friends, and didn't seem to be an issue.
We just never went wine tasting, because it wasn't something that interested him.

There is plenty to do in this world that doesn't involve drinking! :)