Composure was a quality valued by both of Bob's parents. As a doctor, Robert Senior needed to stay composed when treating patients. It was no good to have a doctor who fell to pieces over everything; he'd be quite useless. And of course, Judith needed to stay composed for her performances, and keep stage fright at bay.
Following the wisdom his parents imparted on him, Bob kept his emotions in check as much as he could. He began to make school speeches without fear, he let the insults of his peers slide off him, the way banana cream pies later slid off his face when Krusty threw them at him. Bob very well couldn't smack or throttle Krusty on live television without dire consequences. At best, he would become a bad role model, and at worst, wind up in prison.
Bob managed to keep himself calm when he first announced to the youth of Springfield that he was taking over Krusty's show. No sweaty palms, dry mouth, hair-pulling, or twitchy eyes and fingers. No mad laughter as in the case of his later victory of being elected Mayor; that would have terrified the poor tots. He knew the importance of making a good impression on the children, or else he would have lost any chance of earning their respect. Bob had simply relaxed, cast aside his slide-whistle, and allowed the audience to hear his real voice.
Of course, forcing himself to remain collected all the time wasn't the best thing for Bob's mental health, which had never been perfect in the first place. Within Bob's fragile mind was a "seething cauldron of rage", as he had once eloquently phrased it to the Simpsons and Bouviers. So much negative emotion filled up that cauldron that it could overflow at any time, and it had indeed done so at several points...