The human mind was an odd thing, both strong and fragile at the same time. Even when the mind seemed to completely and utterly snap, there was still something that could keep you going...most of the time, that is. Bob liked to think that something was either strength of character, the desire to achieve a goal, or a sense of duty, as opposed to mere, base survival instinct.
Krusty had been broken by the grim realities of show business long before Bob met him. The only things that kept him going were alcohol, drugs, money, and a crippling desire for an audience. Bob had done his best to stay strong, even through Krusty's abuse. He had a goal that kept him sane: his desire to improve children's minds.
Vengeance kept Bob sane and mad at the same time. He had plunged into the darkest depths of his madness after his family grew to loathe him, and more so after they apparently disowned him. His urge to kill Bart had prevented Bob from killing himself. It was something, at least.
Of course, Bob himself still had moments where something within him broke. After all, he had attempted to take his own life three times. The first time was after his failed efforts to rid Springfield of television. The frustrations of being foiled five times had pushed Bob to try and end his life with a literal bang, or to be more precise, a mushroom cloud. When that had failed, it was Bob's attempts at a kamikaze mission. Bob simply couldn't resist creating some drama and making an effort to accomplish a goal, even when trying to die. Then there was his leap off the Springfield Dam following the genetic experiments on himself, and trying to bash his head in with a rake when everyone thought the missing Bart was dead.
Certainly there would be those who would call Bob a coward, or a sinner, but they wouldn't be so judgmental if they felt they had nothing left. Vengeance kept Bob going, and if he had no-one on which to enact that vengeance, what else was there left to strive for?
On the subject of Bart...he may have been the biggest brat to ever walk the Earth, but the boy possessed a surprising fortitude for a ten-year-old. He was difficult to break. In all of the times Bob had tried to kill Bart, he had never seen the boy cry or surrender. There had been fear, certainly, but never despair. Bart usually at least tried to escape, even when he didn't have a proper plan to do so. And if escape wasn't an option, he still had his usual smart-mouthed defiance.
Bob had been a little taken aback at Bart's relative lack of panic while a hostage on the Wright Brothers' plane. Bart had simply complained about the insects getting into his mouth, even when there was a knife at his neck. Even when Bart learned of Bob's intentions with the plane, Bart had still tried to reason with Bob and get him to spare Krusty, as opposed to panicking or begging for his own life. Bart, of all people, had brought Bob back to reality when Bob was about to kill him and Milhouse.
Ugh, Milhouse. Getting Milhouse to break and do his bidding had been all too easy. It may have amused Bob to see Milhouse crack at the sound of a little light operetta, but at the same time, it was disappointing. There was no challenge as there was with Bart.
As much as Bob hated to admit it, he had to respect Bart to an extent. Bob wished he had such a cool head.
Envy of a beastly little child...Bob could hardly believe he had sunk that low.
This may have been another driving force for Bob's hatred of Bart. Perhaps Bob didn't really want to kill Bart, but simply break him, and wipe that seemingly perpetual smirk off his smug little face. One might say it was a morbid psychology experiment, to see what made even the toughest child snap.