I think, as with most women who feel the same way she does, the issue of trans women in bathrooms is way at the very bottom of the list of concerns for Rowling.

Bathrooms are already mostly private spaces after all.

Higher on the list is communal changing rooms, then prisons, rape-crisis centres, and sports, then the idea that women don't get a say in sweeping changes to the very definition of what they are. And, I think most of all, the "affirmation at all costs" model of trans care that is seeing increasing numbers of teenage girls specifically, having their breasts cut off and taking hormones which affect or remove their fertility.

There's a growing number of these girls regretting their decision because there wasn't enough care taken to ensure they really were trans, and being left with disfigured bodies, facial hair, unnaturally deep voices and fertility problems. This doesn't make me smile.

Women who simply want to have an honest conversation about these issues are being harassed and subjected to abuse and death threats. Compared to that, being called a TERF or even a "person who menstruates" probably isn't a very big concern!