It didn't, necessarily. It could be an independent innovation in both locations.
I kind of find that unlikely considering that "bubbler" doesn't exactly describe what the object in question actually does. I've never really seen a water fountain bubble in any significant fashion.
Actually looking it up shows that it was a trademarked brand name for the original water fountains. The name apparently didn't stick for the product in general, which is the opposite of the escalator, which was also a trademarked brand name originally, but since the general public began to associate the name with any moving stairs the trademark was lost and "escalator" became public domain. There's your useless fact of the day.