The story
From Pooh-Bah, a comic character in the Gilbert & Sullivan operetta The Mikado (1885), formed as pooh + bah, both expressing contempt. The character of W. S. Gilbert's libretto is preceded by the character Pish-Tush-Pooh-Bah (described as “haughty”) in “King Borriah Bungalee Boo” (1866), one of the Bab Ballads, with pish and tush being two other terms of contempt.
Etymology from Wiktionary, CC BY-SA 4.0.