OK, so, stay with me now… This answer is for rounds 2 and 3…

Bobby could potentially beat the Joker, if the Joker has decided against physically harming Bobby, and wants instead to break Bobby’s spirit. This isn’t absurdly far-fetched, because the Joker wouldn’t have much fun simply killing Bobby. Once the Joker realizes Bobby has WEIRDLY strong willpower and resilience, the Joker might enjoy trying to break Bobby, just like he tries to break Batman.

In Season 7, episode 15, “An Officer and a Gentle Boy”, the legendary soldier and killer of fitty men, Colonel Cotton Hill, Bobby’s grandfather, forcibly takes over the military academy Bobby attends and decides to toughen Bobby up. Cotton Hill is batshit insane, and very good at making people feel very bad. If there was a Joker in King of the Hill, he’d have no shins. (If you do not understand this reference, please go watch King of the Hill, a lot.)

First Cotton makes Bobby rake the yard with a fork. Bobby enjoys it. Then, Cotton attempts to make Bobby eat until he pukes. Bobby has no problem with the mass consumption, having previously eaten a 72 oz steak in a mere 37 minutes. Next, Cotton forces Bobby to sit on a giant cube of ice. Bobby melts his way through it, being, as Bobby says, “naturally built for winter.”

Finally, and full-on insanely, Cotton throws Bobby into “the hole” which is a tiny bunker, too small even to stand in, with no food or water. This torture itself broke Cotton after two days. Bobby never tapped. He was released after 3 days, and his first words upon exiting the hole were, “(YAWN) Well, I’ve tried mattress, I’ve tried cement… I’m a mattress guy” to the amusement of all of his fellow cadets, and the outrage of Cotton.

Cotton is vindictive, sadistic, and experienced in the ways of war and torture, and he didn’t put a scratch on Bobby’s spirit. I could see a world in which the Joker, trying similar tactics, walks off after calling Bobby crazy, and laughing at one of Bobby’s jokes.

TL:DR – Joker’s tactics have been tried, left Bobby well-fed and better rested, username relevant.