I love that the author is incorporating real-world concepts like the stats for homosexuality and the lesbian bar as social outlet. It reminds me of Takemiya Jin, one of the few other yuri authors I've seen do that. It makes it easier to relate to the characters as real people rather than romantic fantasy characters (although there's nothing wrong with those).
Is underage drinking at bars fairly common in Japan? All of my underage drinking occurred at people's houses, even in college.
I doubt she's drinking alcohol. I do know bars in Japan have non-alcoholic drinks, and even here in Canada kids are allowed in licensed establishments (although I think they may need to be accompanied by an adult, I'm not sure) so long as they're not served alcohol.
In this case, I'm pretty sure the bartender is familiar with her and other patrons can vouch for her so she'd certainly be allowed in the door at least.