"I must use the bathroom."
Translation:Mi devas uzi la necesejon.
Necesejon (neces + ej + o): "necesa" means * necessary* + "ej" is a suffix that indicates a place or room + o indicates a noun.
The adjective "neces" is the root to multiple other words, like the adverb "necese" with the same meaning, but also words like "necesi" that means "to be necessary" and "neceso" which means "necessity".
The necesejo is the "room for necessities".
The words you mention with ban- are places for bathing. Last week at NASK, we were staying in dormitory rooms with attached rooms for toilet and bathing. A woman was unable to use her own room because someone else was in there. She asked me if she could use my "banĉambro" and I was honestly shocked. There I was on a trip without my wife and some woman wants to take a shower in my room. After a few seconds, it clicked that she really needed to use the toilet and (given the often more urgent nature of such requests) this seemed perfectly reasonable.
Summary - don't say banĉambro when you mean necesejo.
OK, I think I'm piecing this together. I have found "banĉambro" and "banejo" in online dictionaries on my own; Duolingo hasn't introduced them (yet). Therefore, it seems that "banĉambro/banejo" are perfectly good words for "bathroom", but not in the use here (although this English use is arbitrary). I would translate "necesejo" to English as "restroom", or even "toilet", meaning the whole room/facility. Perhaps a change to the English sentence would be an improvement?