I know I'm going to catch crap for saying this, but I still say that if you have the voice and carry yourself right, it almost doesn't matter what you look like physically, no one's going to question you. That's one of the reasons I started rigorously working on my voice months before I came out fulltime. The mannerisms and such came naturally, voice was difficult, but BOY was it worth it.
Case in point... How much people-watching do you do? And I don't mean ogling pretty women as they walk by, unfortuntely I know plenty of transwomen who do that... I mean, just subtly watching what women wear, how they do their makeup, how they walk, how they talk... I spent my entire life surrounded by women but I still people-watch to see what people are wearing and what they are doing. Now... Back to my point... Look at a LOT -- not just a few -- a LOT of the women that pass through the doors at your local department store and see how feminine a lot of them look. They don't. I've speculated that about 20% of women look pretty d*mn unsightly. The difference between them and the average transgender woman who is struggling to pass is, they don't question their gender. I don't mean that as an insult to any of you. I hated the beginning and in between stages because I knew I didn't pass well and I still question my looks even though I never get read.
Remember that if you're on 'mones for any length of time your looks are probably changing by the month. Now is the time to work on the other things that will make or break you and stop worrying so much about physical appearance. It's the one thing you can't do anything about, yet it's the number one thing transgender women obsess about, many times forgetting about all the other little things that will help them pass. My #2 tip? More makeup and jewelry doth not a woman make.
I hope I don't sound preachy or insulting because I'm definitely not trying to do so. Going back to the original point, public bathrooms aren't going to be a big deal if you work on the things that matter NOW instead of waiting until you're fulltime or not working on them at all. And as always, YMMV.