Question

Yo quiero la habitación individual con un cuarto de ____________ privado.

Answer 1

If we are talking about a private room at a hotel or in a house, we generally would ask for a private bathroom so the sentence should be complete in the following way :

Yo quiero la habitación individual con un cuarto de BAÑO privado.

It is not possible to say hotel or cuarto because it is already implied in the context. We need to refer to something inside the hotel room.