Restroom is public only.
Bathroom is (usually) at home, or in a hotel room.
A term still inscribed in Canadian schools as late as the 1950's, but now usually British, is lavatory.
There's a perfectly good word toilet, but it seems to have become something that requires a euphemism.
I would suggest a school washroom. Of all of the terms, it seems the most neutral and most nearly universal.
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