The bathrooms there always seemed to be reather empty to me.
I'd say if any part of the second costume would fit under the first, go for it. Other than that, I'd say bathrooms are much quicker than running to your room, unless perhaps you have a low-level room in the same hotel... If you're not shy, in my experience people will understand if you change really fast in the corner if every stall is filled up, but wear tasteful underwear and stand away from the door.
I'd say if any part of the second costume would fit under the first, go for it. Other than that, I'd say bathrooms are much quicker than running to your room, unless perhaps you have a low-level room in the same hotel... If you're not shy, in my experience people will understand if you change really fast in the corner if every stall is filled up, but wear tasteful underwear and stand away from the door.