The bio (Orson Welles: The Road to Xanadu, by Simon Callow) says that Welles was at the school for just a short while, but I don't think the author gives an exact length of time. He does mention Welles' claim that when the head of the school made a sexual advance, Welles jumped out a window. That may or may not have happened, as the author notes it is often hard to separate fact from fiction when Welles tells stories about himself. In any event, Welles next attended the Todd School in Woodstock Illinois.
As for the Washington School, one writer claims: "As a child, Welles was thrown out of the Washington School in Madison, Wisconsin, for wearing a Halloween costume so disturbing that his teacher ran screaming from the room; he must surely have been imitating [Lon] Chaney." See http://www.albany.edu/writers-inst/webp ... 04n10.html
The bio I'm reading doesn't mention that claim.