They bullying in the book is evident on different levels. You have the more childlike bullying that Scout gives to her cousin, Walter Cunningham, and others that speak poorly of her father. The victims here either receive the satisfaction of having riled Scout, or a good beating. There is the "bullying" that Jem gives Scout when she whines about not wanting to harrass Boo Radley, which is more in the form of mockery or dismissal, and prompts her to exhibit her bravery.
The more serious examples of bullying occur in regards to the Tom Robinson case. Atticus indicates that a Cunningham on the jury did his best to stand up for what was right, but most likely peer pressure and bullying got him in the end; the effect was a guilty conviction for Tom. Bob Ewell bullies Atticus and his family, first verbally, and then through his actual attack. The effect of that attack was huge; Boo Radley saved the day, Scout and Jem were traumatized, and it was an event that they pondered for the rest of their lives. Tom Robinson himself was bullied by the Ewells in their false testimonies, and when he was shot at the end. His family is forever impacted by those events.
There are many instances of bullying. some pretty harmless and others life-changing and cruel. Either way, they all had an effect on the victims one way or another.
In the narrative of To Kill a Mockingbird, there is both physical and psychological bullying.
Chapter 2: Miss Caroline criticizes Scout for her ability to read. She belittles Atticus's teaching of Scout at home, and instructs Scout to tell her father to no longer teach her how to read because he does not know what he is doing.
Chapter 5: To bully someone is to torment that person, and in Chapter 5 Atticus scolds the children for "tormenting" Arthur Radley after Jem and Dill have attempted to communicate with him by attaching a note to a fishing pole and putting a note through a window.
"I'm going to tell you something and tell you one time: stop tormenting that man."
Chapter 8: Bullying also involves ridiculing a person. The children construct a snowman after a freak snowstorm. Because this snowman resembles Mr. Avery, Atticus scolds the children:
"You can't go around making caricatures of the neighbors."
Chapter 9: Scout retaliates against Cecil Jacobs, who tries to browbeat her by announcing in the schoolyard that "Scout Finch's daddy defends n*****s."
Also in this chapter, Cousin Francis calls Dill Harris "a little runt," and he tells Scout that he supposes "it ain't your fault if Uncle Atticus is a n*****-lover besides."
Further in this chapter, Scout feels that her Aunt Alexandra has attacked Atticus when she has reportedly said that "he is ruinin' the family," and Cousin Francis calls Atticus "...nothin' but a n*****-lover."
Chapter 11: Mrs. Dubose certainly bullies the Finch children as she "hollers" insults at them when they pass by her place, saying that Scout will work in a diner and Jem will not amount to much either.
Chapter 14: Atticus defends Calpurnia against the intimidation of Aunt Alexandra. He will not permit her to fire his faithful housekeeper, whom he considers a member of his family.
Chapter 16: The mob from Old Sarum attempts to bully Atticus into releasing Tom Robinson to him so they can hang him.
Chapter 17: Mr. Gilmer attempts to browbeat Tom Robinson when he takes the stand and testifies, accusing him of desiring Mayella: "Had your eye on her a long time, hadn't you, boy?"
Chapter 24: Mrs. Merriweather's none-too-subtle comments about Atticus as being "Good, but misguided" in his attempt to defend Tom Robinson are cruelly said in the presence of his sister, Alexandra.
Chapter 27: Helen Robinson, who has been given a job by Link Deas, is forced to walk nearly a mile out of her way to work in order to avoid going past the Ewell place, where Bob "chunked at her" or "followed her."