The novel contains a number of descriptions of Arthur (Boo) Radley as having characteristics that we would regard as representing shyness; however, the novel contains but 2 references to Arthur (Boo) Radley specifically using the term "shy". Both instances are found in CHAPTER 30. In order of importance, the 2 instances, with quotations, follow:
1. Sheriff Tate refers to Arthur (Boo) Radley as shy near the close of CHAPTER 30.
Recall that Bob Ewell attacked Scout and Jem; and a man [Arthur (Boo) Radley] was seen by Scout carrying the injured Jem to the Finch house. Later, Bob Ewell is found dead near the place of attack. Atticus knows that either Jem or Arthur (Boo) is involved in Ewell's death in the scuffle, and he is unsure what should be done. Sheriff Tate does not share his uncertainty. He fully intends to report that Bob Ewell fell on his knife. During the course of his conversation with Atticus, Sheriff Tate says the following:
__(Sheriff Tate) "I never heard tell that it’s against the law for a citizen [Arthur Radley] to do his utmost to prevent a crime from being committed, which is exactly what he [Arthur Radley] did, but maybe you’ll say it’s my duty to tell the town all about it and not hush it up. Know what’d happen then? All the ladies in Maycomb includin‘ my wife’d be knocking on his [Arthur Radley's] door bringing angel food cakes. To my way of thinkin’, Mr. Finch, taking the one man [Arthur Radley] who’s done you and this town a great service an‘ draggin’ him with his SHY [emphasis added] ways into the limelight—to me, that’s a sin. It’s a sin and I’m not about to have it on my head. If it was any other man, it’d be different. But not this man, Mr. Finch."
2. Scout refers to Arthur (Boo) Radley's smile (and general demeanor) as shy at the beginning of CHAPTER 30.
During the attack by Bob Ewell, Jem's arm is broken and he is carried to the Finch home by Arthur (Boo). As CHAPTER 30 begins, Jem is asleep in his bed. While in Jem's room, Scout recognizes that a person in the room is Arthur (Boo). Therafter, the following text appears beginning with Atticus saying to Scout that she should not refer to Arthur Radley as "Boo".
__(Atticus) "Mr. Arthur, honey. ... Jean Louise, this is Mr. Arthur Radley. I believe he already knows you."
__(Scout as narrator) "If Atticus could blandly introduce me to Boo Radley at a time like this, well—that was Atticus. Boo saw me run instinctively to the bed where Jem was sleeping, for the same SHY [emphasis added] smile crept across his face. Hot with embarrassment, I tried to cover up by covering Jem up."