One of my worst dating experiences was when a girl took me to a bar, in which her ex served us as a waitress. You want to start fresh, without any baggage or creepy conversations. Some people don't give a crap where they are or who they're with.But if you go to a place frequented by the gays then it doesn't really matter either way. I'm not saying tell her your life story but just be yourself.You can get to know someone and let somebody get to know you without going to deep. This isn't Lesbian Dating 101, because there's no such thing.
You don't want to accidentally wear matching outfits either. So, I guess your best bet is to just go smart-casual for the first date or wear what you think would be appropriate for the venue. Anyway, if you're a woman on a date with a woman it's a good idea to just split the bill, or at least suggest splitting the bill. But you do need to have an idea of where you both stand from day one. Nor should you be talking about hook-ups or mutual people you know from the bar scene or anything like that.
And above all you should wear what you're comfortable in, something that makes you feel good. That's surely a question that's baffled lesbians for centuries. I would like to think that straight people have the same dilemma nowadays in the age of gender equality. As you well know, the community can be quite tight-knit so it would be pretty gross to talk about other people.
If you're like me you'll have absolutely no idea what to wear. If it's the other way around then you know she's only into getting nasty with you, so she's great if you're looking for a friend with benefits.
I wouldn't want to turn up in jeans and a T-shirt when she's dressed all fancy in a dress or a blazer or something, and on the reverse I wouldn't want to get dressed up to the nines when she's chosen a chilled outfit. Plus, by splitting the bill you're starting out in a good place, on equal grounding. If you're the first woman she's ever been on a date with, then you have to decide whether you're ready to take her under your lesbian wing and so on. I'm not saying you should be finding out whether she wants marriage and kids some day, cringe.