Not sure of they exactly fit the "bully tickling" criteria but there were two animated scenes I always liked that certainly touched on the issue.
One was the classic Flintstones episode where blowhard Fred is arguing with his burly neighbor, who proceeds to drop the stone fence dividing their yards onto Fred's ankles, leaving Fred's bare feet pinned on his neighbor's side of the fence. Fred continues his threatening bluster then stops abruptly and becomes panicky. "Oh no ... you wouldn't do that ..." he stammers hesitantly, "You wouldn't ... tickle my feet, would you?". Well, needless to say, this was not the smartest thing to say. The neighbor begins to tickle Fred's helplessly displayed soles, taunting him by saying, "kootchy kootchy koo" as Fred dissolves into joyless laughter.
The other was one of the Fifties Popeye's in which Popeye dispatches Brutus with an uppercut that sends him high into the air, only to come crashing down in the zoo - specifically, the laughing hyena's cage. The hyena looks at Brutus a moment and starts laughing. Brutus looks at the hyena and seemingly inexplicably starts laughing ... the reason becomes apparent as the camera pans to the side. Popeye, having defeated his rival, now humiliates him. Popeye has removed Brutus' shoe and is very playfully drawing his index finger up and down Brutus' bared sole. The bigger man's toes wiggle spasmodically and he cackles hysterically. Eventually, all in the scene are laughing - the hyena (his nature), Brutus (ticklish) and both Popeye and Olive who both find Brutus' predicament terribly amusing!