So any world leader (an equal?) should not bow, but everyone else should. Is that right?
I've been on the Emperor's grounds in central Tokyo, but I've never met any of the royal family in person. Other than being angrily corrected by my late wife - "It's Michiko-sama!!" in speech, I never had exposure to that level of protocol.
I would bow to him in Japan just because that's the culture, but not that low.
(I also genuflected to my current manager when he was named to the position. I would never do that outside of the US).