Character Analysis
Jim Rangely
Technically speaking, Jim Rangely, Bart's dad, isn't in the book. He's already gone at the beginning of the story, having left his family to go live with his young mistress, and before Chapter 1 is over, he's killed in the attacks on the World Trade Center.
Still, his presence—or the lack of his presence—shapes the book in profound ways. Bart misses his dad, but also he's angry about the whole abandonment thing. This makes his death really complicated for Bart (to really dig into this, swing by Bart's page elsewhere in this section). From the little we do know about Jim, it seems like he was a loving dad who wasn't perfect. We also know his relationship with Bart was strained after he moved out, but that he tried to contact his son regularly.
Would father and son have grown close again, given time? There's no way to know.
Dr. Bratton
Dr. Bratton is the headmaster of Baileywell—a man with a "delicate, chirpy grace" (3.23). He's a minor character, so we don't get to know him very well, but we see enough to gather he's a bit insincere. While Dr. Bratton is the head of a school that's notorious for its bullying problem, he seems completely unaware of (or perhaps unwilling to admit) the problem until he finds Bart stuffed in a locker. Also, the fact that he never bothers to learn Bart's real name—Dr. Bratton refers to him as "Brad" throughout the book—suggests that the headmaster isn't a particularly caring person.
Mrs. Straus
Mrs. Straus is the social worker that helps Bart coordinate his volunteer work at the hospital. Though she's a minor character, the actions we see suggest that she's kind and caring. In some ways, she's in tune with Bart's needs; she's patient and attentive as he navigates three separate freak-outs. At the same time, she's a little out of touch with what's appropriate when she has Bart visit with Stimmer, a patient who's known for asking visitors for a part of their livers: "I'm sorry," she tells Bart. "I should have seen it coming" (10.101). Yeah, she probably should have.
Tyro's Parents
We only really meet Tyro's parents once, when they're called in for a meeting at Dr. Bratton's office and we learn that they're the anonymous donors who have been funding Bart's education at Baileywell. Tyro's mom says next to nothing, but she seems sympathetic to Bart. Tyro's dad is an alpha businessman type. When he clears his throat, "you could tell that he was used to having that sound silence an entire boardroom" (9.34). Still, he's not a complete jerk. He and Mrs. Bergen are funding Bart's scholarship and the Reach Out volunteer program, which are both good causes.
Assorted Nerds
In a book about bullying, it's reasonable to expect a certain number of nerds, and Bullyville doesn't disappoint. Of course, the main nerd is Bart—a sensitive kid who tries to joke with his bully about George Orwell (4.47).
But there are also a lot of minor nerds surrounding Bart. Bart sees himself in these nerds, and it makes him hate them a little. He describes the "losers" (4.32) on his bus as "a casting call for the latest Hollywood nerd extravaganza" (4.31). And then there's Bern, his mom's colleague, who disgusts Bart. Bern "didn't just remind me of the geeks I rode to school with," says Bart. "He reminded me of me. […] It made me hate him" (7.38-7.39). Unfortunately for the nerds in this book, they're mostly scapegoats for Bart's pent-up self-loathing. Poor guys.