It really has to be "how do I know you are trans", not the other way round.
The problem is, thanks to TRAs, it really needs to be more than that now. As a PP said, previously TWs would use a womens bathroom unchallenged.
If this all gets formalised as e.g. TW with a GRC can use female bathrooms, then they'll need to have their GRC handy every time they go.
Or, more likely, the line has to be drawn at either "everyone who identifies as a woman" though that would exclude lots of women or alternatively "female sex".