you shouldn't say "sorry" but "excuse me". sorry expresses regret while escuse me is to attract someone attention. once again I'm here to learn Danish but I don't want to mess up my English. exercises should be prepared by linguists who have perfect knowledge of both languages.
If you need to use a bathroom, definitely when out and about (restaurant, station, etc) you'd ask for "et toilet."
Really the only situations where I see "et badeværelse" is when talking about the rooms in a house / apartment. As in "Der er et stort badeværelse til venstre." So not a thing that tourists would normally encounter.