The closed-door part is a different behaviour and worth separating, because it generalises.
What cats object to is not the room, it is the barrier and the loss of information. A cat that has never once entered your study will still complain at the study door if it is closed, and lose interest the moment it is opened, often without going in. The interest is in access, not the destination.
So the bathroom gets a double dose: it is the room she wants to be in and it is the room where the door actually gets shut. Every other room is open, so the behaviour never appears there and you never notice it.
A cheap test if you are curious: shut a different door for a week. Most people find the complaining follows the door rather than staying with the bathroom.