"A Bully For Bugs" is the fifth episode from the second season. It features Baby Elmer as the central adversary.
Floyd is preparing to take the children to a candy shop to get candy by giving each of them a quarter, so they could get the candy of their choice.
The children, unaware that they are passing Elmer Fudd by, enter. Tweety, for reasons he doesn't know, wants a candy worm, Lola wants taffy, and Sylvester wants a lollipop. Bugs comes first asking for gumdrops. Outside, he begins eating when Elmer asks him for some. Bugs tells him he isn't sharing his candy with every kid that comes down the street, because then he wouldn't have any. Just as he's about to eat more, Elmer takes it away, even the bag. He says that if he shares his candy with every rabbit he meets, there wouldn't be any left for him. He taunts Bugs.
Bugs, afraid to admit what happened to Floyd, claims to have eaten the whole thing, though he feels left out because everyone else gets candy. Floyd gives him a nickel as the change from his quarter. He tells him to make it last this time. Bugs gives Candy the coin, only to get very little of it. Again, Elmer demands Bugs give him more. Bugs tells him what he has isn't enough to share, but Elmer takes it anyway, as he "wasn't planning on sharing anyway." He then threatens to get Bugs if he tells anyone about it. So, when Floyd asks him what happened, but instead of telling him what happened (due to the threat), he claims he dropped it on the ground and had to throw it out. He pretends nothing is wrong.
Tweety, feeling sorry for Bugs, gives him a marshmallow rabbit, but Elmer bothers him again. When Daffy comes over, Bugs takes him outside to see what happened. Again, Elmer demands all of this candy. Daffy, having a chocolate duck, is involved in the argument he starts, saying it is bitter. They argue, and Bugs tricks Daffy into deciding to give Elmer the chocolate duck. Although this works, Elmer still takes the marshmallow rabbit.
Back inside, Daffy tells Bugs to tell the other kids what happened. Upon fearing that he would get caught, Bugs refuses, so Daffy begins. Not wanting this to happen, Bugs finally tells them what happened. Elmer is familiar to the other kids, as once, he attempted to take Sylvester's blanket, took away Lola's ribbon and kept it away from her, knocked Melissa's piece of pie on the ground, and pushed Tweety down in the sandbox. Without Taz or Petunia deciding what he did to them, Bugs decides he had been picking on all of them. Melissa, Sylvester, and Daffy plan violent ideas by drawing it on a blackboard.
Melissa decides to paint a target on his head and drop so many pies on it that he cannot stand up due to the weight of all of those pies. Sylvester decides to put him in a giant milkshake machine so that he would end up looking like a puzzle with the pieces in the wrong places. Finally, Daffy decides to get "the world's biggest rubber band" (a giant slingshot, actually) and send him to the moon so he would have to pick on green mice. Lola and the other kids (except Bugs) think he deserves that.
Bugs disagrees because he didn't have candy and they did, so, he decides on having them help him out on them giving all their candy to Elmer.
Surrounding Elmer, Bugs and his gang walk over to give all of their bags of candy to him. Thinking that nobody has ever been this nice to him before, Elmer begins to cry. This attracts Floyd, whom Daffy tells that Elmer has been picking on them. Floyd has Elmer blow his nose on his handkerchief, and then is about to put it in his coat pocket, but remembering what was done, he discards it instead. He asks Elmer for his name, and he reveals it. After Floyd asks him if he's been picking on the others, Elmer says he did "maybe a little," but Bugs tells him it was a whole lot. Elmer says he felt really left out because Bugs, Daffy and the rest are "such good buddy-buddies." Floyd tells Bugs Elmer was acting like a bully just to get attention. Bugs tells him that they thought Elmer needed a friend, so they gave up all their candy. Floyd commends Bugs for how he handles the situation, but tells him he could have come to him. Bugs tells him he knows now. Floyd tells Elmer that although the latter had learned his lesson, the former was still going to have to talk to the latter's parents about how he was misbehaving. Elmer sadly agrees. Daffy and the other kids forgive Elmer for his deeds, and Bugs offers him an invitation to Granny's for a playdate. Elmer accepts willingly "as soon as they finish all their candy." He then gives the kids their candy back and they begin eating it.
- It is possible that Candy, the lady who was working at the shop, is Floyd's girlfriend. Otherwise, she may just as well be a friend of his.
- Bugs and Daffy arguing over whether Elmer should (respectively) eat Bugs' marshmallow rabbit (which Tweety had given to him) or Daffy's chocolate duck is just like their older counterparts arguing over whether it is Rabbit Season or Duck Season, meaning whether Elmer should shoot one or the other Bugs Bunny Saves Santa
- In this episode, Daffy drew blood (not colored, but still shown.) after Elmer got flung to the Moon. Although this happened, nobody said a word about it.