In England we don't usually talk about restrooms, and bathroom usually means a place where you have a bath - it may or may not have a lavatory.
There's fürdőszoba, which is the actual bathroom with shower and/or tub and all. But no, mosdó is on its own. You could say mosdószoba, but it's pretty redundant.
But the asking person was meaning a washroom , isn't it clear ? Don't argue!..