The most important scene of bullying is Assif's rape of Hassan. This is a short, but clear scene at the very end of the Kite running contest. Amir sees the attack, but does nothing to stop it, and instead of treating Hassan the same or better after the attack, he actively seeks to push Hassan and his father away. He makes false accusations, and Hassan and his father ultimately choose to leave Baba's employment. Amir, in his childish way, is trying to relieve himself of his guilt by pushing away the constant reminder, the actual presense of Hassan. Amir's guilt is pricked by the fact that Hassan never speaks of what happened; he gives the kite to Amir in an act of unwavering loyalty; and he continues to be the kind and gentle person that he always was. The entire novel hinges around this event. Amir spends the rest of the novel trying to live with these actions. When he is called upon to return to Iran and to rescue Hassan's son, Sohrab, he does it because he is trying to atone for his guilt in all that happened before.
Although Assef's bullying of Amir and Hassan is the most obvious example of bullying in The Kite Runner, there are other examples.
- AMIR BULLYING HASSAN. Although Amir spends a great deal of time with Hassan, he can never bring himself to consider him as an equal or a friend. Hassan is the family servant's son, and Amir never forgets this. Hassan probably never considers Amir's directives as bullying, but Amir was aware that his orders would always be followed.
- SANAUBAR BULLYING ALI. Ali was certainly a henpecked husband, and his wife looked down upon him before finally deserting him.
- FATHERS AS BULLIES. Both Baba and General Taheri rule their children with iron fists--particularly the General and his control over Soraya and his wife.
How do you define bullying precisely? If you are after examples of bullying during Amir's childhood, that is one thing, yet if you are looking at violence between characters, that is a much wider issue that occurs throughout the novel in a number of different contexts. I will assume you are referring to bullying that occurs between children in the first section of the novel.
Of course, the biggest example is Assef and how he picks on both Hassan and Amir. This of course threatens to move into physical violence but definitely is an example of psychological bullying. Consider this description of one little run-in that Amir and Hassan had with Assef and his gang:
Assef slipped on the brass knuckles. Gave me an icy look. "You're part of the problem, Amir. If idiots like you and your father didn't take these people in, we'd be rid of them by now. They'd all just go rot in Hazarajat where they belong. You're a disgrace to Afghanistan."
I looked in his crazy eyes and saw that he meant it. He really meant to hurt me. Assef raised his fist and came for me.
Of course, as the narrator himself identifies (but in his older, maturer self who is looking back at the action), Assef is a psychopath who delights in violence, but clearly Assef is bullying Hassan and Amir because of Hassan's race. It is only the bravery of Hassan in threatening to blind Assef with his sling that prevents Amir being beaten up by Assef.
Therefore, if you are looking for examples of bullying during the first stage of the novel, you need look no further than Assef and his cronies who intimidate and bully Hassan and Amir because of his association with Hassan because of Hassan's race.