A woman is statistically much more liable to be abused by a (cis, straight, etc) man in public transportation than by a transwoman in a restroom. Since "once is once too many", I am assuming you are vigorous defender of banning cis men from buses? This is getting silly.
As
SF Kosmo
pointed out, the notion that people "fake" being trans to molest others in restrooms is pure culture war paranoia repackaged and reheated from past moral panics. It is statistically so rare as to be almost nonexistent.
I am sure it has happened somewhere, as other unlikely things have: nuns doing orgies below the holy cross, climbers having sex with goats in the dark thinking it's their partner, French mimes committing genocide in foreign battlefields..
One does not organize society based on statistical irrelevances. Trans people exist, and are deserving of all the necessary protections so they can live their lives in peace and flourish. The vast, overwhelming majority of trans people will never commit any crime more serious than a parking offense in their entire lives.
Now, does that mean that lady should have lost her job based on a 7 year old tweet? I don't think so. One can argue that point without resorting to the same tired bathroom nonsense.