I think 'loo' should be an acceptable answer here. It is what we say most in British English.
That is a regional thing. 'Loo' is not common everywhere in Britain. Where I come from 'loo', like 'lavvy', is a humorous, slang form, and 'toilet' or 'cloakroom' is the norm when speaking to a stranger. I would excuse myself from a room in a friend's house by going to a 'loo', but would not use the word to anyone who I did not know well enough to not already know where their toilet is!
From what I've read/seen so far, ванная refers to the bathroom in a person's home or possibly one in a hotel/inn. Туалет literally means "toilet". From other discussions on Duolingo about toilets and bathrooms (I think either in the French course or Spanish course or possibly both), it seems that North Americans generally don't ask for the "toilet" when in public or when visiting someone's home. So, it appears that the Russian Duolingo staff decided to go with "bathroom" since some people use that word regardless of looking for public facilities or visiting someone's home. I, like other Canadians, use the word "washroom" when speaking of public facilities. I generally use the word "bathroom" when referring to the room in a home. (See https://en.wikipedia.org/wiki/Public_toilet for other names for "public toilet").
It's a bit confusing for me, since in most of the cases (what i've encountered) the toilet and the bathroom were in separeted rooms, so the different names seemed to be proper. By the way i have to admit your truth, here in Hungary when speaking in a formal way they use to say something that could be mirror translated as washrom. :)
[ There's an Entire Book on Dating and Bathroom Etiquette ‧ ‧ www.glamour.com/story/how-to-poo-on-a-date-book ] ‧ ‧ [ of the least discussed etiquette topics is bathroom etiquette ‧ www.thespruce.com/bathroom-and-restroom-etiquette-1216664 ‧
Bidet, bed pan, commode, toilet, urinal are terms serving no other purpose than for human physiologic gastro-intestinal, evacuating bowels, bladder and stomach regurgitation activity. Any disruption to continuous gastro-intestinal peristalsis and valsalva functions are soon life threatening, just the same as disruption to cardio-pulmonary functions, but gastro-intestinal functions are some of the least condoned disclosure topics in polite company. Such activity is almost never welcome as a discussion topic in polite company so the associated facilities serving the physiological realities tend to be restricted to indirect references also.
A few of the more delicate euphemisms for toileting activity: ‧ [ Going to; powder noses, freshen lipstick, touch up makeup, fix hair ] ‧ [ Going to; chase rabbits, see a man about a horse ]