Caitlyn/Bruce Jenner: Choose One, Then Flush

There's a new bar in L.A. that guides people to the bathroom with more than the traditional "men's" or "women's" sign ... the guide is one person with 2 identities.

Nickel Bar in West L.A. greets gents with the famous Bruce Jenner Wheaties pic, and ladies with the big Caitlyn Jenner "Vanity Fair" reveal. You're looking at both doors in the pic.

BTW ... it's not an LGBT bar.

So we gotta ask ...