Australia/New Zealand here.
Just about everyone I know, myself included, simply says 'the toilet' (or 'ladies/men toilets' if asking for directions in public), whether it be in public or a private home. Occassionally 'loo', 'dunny' or 'bog' are used, but usually in a joking way.
Most buildings/homes here contain the toilet in a separate room to the shower/bath/vanity area, so asking to use the bathroom would be like asking to use the kitchen in a home when you actually mean the completely separate dining room. If someone came to my home and asked to use the bathroom I'd wonder why on earth they wanted to have a shower or bath during their visit.
That said, our downstairs area has a very large room that contains a toilet, vanity and shower, so technically it is a 'bathroom', but so far all visitors have just referred to it as 'the toilet', as that it was it's mainly used for.