The Bishopper Bounce is a paralell version of Tigger, seen by Piglet. He is King Pooh's bishop, and lives in Chess Land. He only appeared in the The New Adventures of Winnie the Pooh episode A Knight to Remember.
He found Piglet and thought him to be a knight, so took him to King Pooh. Piglet was then sent to fight Eeyore the Dragon and the Bishopper Bounce said goodbye to Piglet when he returned to his world.