I usually go to disabled toilets, if there's no-one in there and no-one waiting. Otherwise, like a crazy person, I wait. I can't deal with going to the female toilets or the male toilets. I went into the male toilets once and I freaking panicked. Stayed in the cubicle for a good ten minutes until no-one was there and ran out. I don't pass well enough, especially with my voice, so justifying it with a "What?" is a little hard. Having said that, I know it's mostly in my head. Working on it. Sometimes I'll go in with a dudefriend or my boyfriend, but only if they need to go, too.
Side note; on the 'fanny' thing, at least with where I grew up in rural Australia, it was one of those slightly more innocent sounding words kids were told to use instead of vagina. We're pretty British in our word usage but it does tend to get filtered by our crudeness, especially in... the outback? I want to say outback, but really it's just kind of a little bit out back, but not far enough that you'd get lost for years and/or die.