In Norway is it more common to ask where the toilet is as opposed to asking where the bathroom is?
You could ask for either "toalettet/doen" or "badet", but beware that in some houses these may actually be different rooms. I would not ask for "badet" in a public building or similar, as their facilities are usually limited to actual toilets and thus wouldn't be referred to as "et bad" in Norwegian.
Asking for the toilet is not in any way embarrassing in Norway, so there's no real need to pretend you're just off to wash your hands. "Toalettet" does sound a little more refined than "doen", so that's usually a good choice.
P.S.: The literal translation "baderommet" would not be used in this context.