The same way: "ez a fürdőszoba". In practice there is no confusion since you can usually tell whether a person meant to utter a whole sentence ("this is the bathroom") or just a noun phrase ("this bathroom"). As the Hungarian phrase here is capitalized and ends in a period, it also seems likely that Duolingo wants you to interpret it as a whole sentence ;-)
When showing people around a house I would probably say it more like "ez itt a fürdőszoba"/"this here is the bathroom". That would not be ambiguous at all.
So, just to make sure that I'm getting this right, the answer to the question "Melyik fürdőszoba?" would be "Ez a fürdőszoba." meaning "This bathroom (period)"?
Cool! I was right to report it as a legit answer, it seems. One small step for Duo, big one for me :)
if we say This is A bathroom, can we say: 'Ez fürdőszoba' and 'Ez egy fürdőszoba' ?
Normally I would use the latter: Ez egy fürdőszoba. The former might work in some contexts, but I can't come up with a convincing example.