Kitty,
Your whole post brought up a well of memories from last year for me! It's one of the toughest parts of transitioning, for sure. I hope I can offer some good advice.
You don't need statistics, data, or a well-formulated argument to win in this situation. I'm not normally the type to confront anyone without a careful deconstruction of the other person's viewpoint-but here is different. You're just using the bathroom-you haven't been challenged to a debate, you haven't asked for there to be a conversation about your gender. You, like everyone else, are in there to do your business and then get out.
If someone comes up to you and says "what are you doing here, you aren't a woman", just correct them. You ARE one. If someone asks if you're there to molest their children, tell them the truth: that you aren't. All of the statistics, science, and logic in the world won't help you here-nobody wants to argue in a bathroom, and bigots have a lovely habit of finding ways to circumvent the most solid of arguments to maintain their ignorance. Just tell them the fact of the matter, and leave it at that-any more than that is simply lending validity to their own insular mindset. All they have is their conviction. Use yours, it's all you need.
I Hope this helps!