Actually, you don't.

You don't even have to feel like a woman to enter a woman's room, you just have to say you identify as a woman.

"Substantial steps towards looking like a woman." What does a woman look like? A woman looks like whatever she chooses to look like. Actually, she sort of looks like me after Taco Tuesdays where I have to use the restroom really badly and all the stalls in the men's bathroom are full.

If you are demanding that a "real woman" make herself subservient to what society thinks a real woman should look like, or maybe even get a note from a doctor diagnosing gender dysmorphia, I would advise you to check your cis privilege. /s

Go to a state that doesn't have a bathroom bill and walk into the women's room claiming that you feel like a woman and let me know how that works out for you.

Sure. Do that in any company bathroom and nobody will say anything.