"Ik heb een badkamer nodig."
Translation:I need a bathroom.
No, in Dutch we're not afraid to actually say toilet or wc, if somebody talks about the badkamer they actually mean the thing with een bad, een douce en een wc (a bath, a shower and a toilet), not a substitute for toilet. If somebody would say Mag ik de badkamer gebruiken? I would expect them to take a shower.
The same is true here in the UK - we don't ask to use the bathroom when we need to use the toilet. Neither do we use "little boy's/girls room".
That's not to say we don't use euphemisms ("convenience" is one, while "to powder my nose" is used to mean "going to (use) the toilet") but most people just say toilet in all but the most polite of circumstances.
The only time we'd generally say "bathroom" here is when asking where it is in someone else's house, since the bathroom is usually where the toilet is. We'd still say "Can I use your toilet?" or something to that effect to ask permission.
Oh euphemisms are absolutely used, particularly by older/posher people, but in my experience bathroom doesn't tend to be one of them, or at least not in restaurants etc (i.e. where there no bath). It's at least uncommon enough that when bathroom is used to mean a room with only toilets/sinks it comes across as conspicuously American (as do little boy's/girl's room and restroom). In fact, the "room with a toilet (but no bath/shower)" definition is listed by Wiktionary as chiefly US, by Oxford as North American, by Collins as [US] and by Chambers as especially N Amer
Loo, lavatory, WC, facilities etc are all more common among the posh/polite, while toilet(s), bog(s), lav(s) etc are more often used in other social circles. It's certainly possible that bathroom is used like that by some people or in some places, but I have yet to come across it and it is seemingly absent from the media.
My father (British) tells a story from years ago (when it was still possible to mend your own car) that he arrived at a house with his hands covered in oil and grime from having to do something to the car. He asked for the bathroom and was shown the toilet which, of course, did not have a washbasin and soap - which was what he really needed to wash all the oil off his hands.
For a more recent example, here is a headline from the Daily Mail in 2015: "Why CANT you stop going to the bathroom after a few drinks?"
I also don't know what I tried to say months ago, so I adjusted my post. :)
I see you are level 14 in German so presumably the concept of separable verbs isn't alien to you. I don't know if this is technically a separable verb, but it is certainly analogous, and nodig hebben can certainly be thought of as a single unit. If it is the logic of that combination that you are having trouble with then try thinking of it as "have need of" rather than simply "need".