If it's a public "restroom" no way I'm saying bathroom. I say that when I talk to Americans, but just if it is in someone's home. I would probably say restroom or lavatory. Informally I'd say the loo. Also informally I let my Scandinavian upbringing take over, I say I need to go pee. Yes, we actually TELL people what we are going to do in there, especially peeing.