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.