You need to check the laws of your state and city. If the state doesn't have a law, your city might.
What matters, at least ethically, is that you're presenting as female, passing isn't required: if you're presenting as male, you can't use the female bathroom.
At least in Canada, there's widespread recognition by our human rights councils that people are allowed to use the bathroom for the gender that they're presenting as. But, of course, this doesn't stop people flipping out or discrimination. This is one reason why I'm part of a campaign (with faculty members on the equity committee) to have signs put up in every bathroom stating that policy position. This way, if someone makes a fuss, the TG (or regular) person can just point at the sign and say, "Take it up with the University." These sorts of signs should be in EVERY bathroom, and if this gets instituted here, I hope that I can advocate for its wider adoption within the community.