He works with Tori in the tattoo parlor. He and Tori are the only ones there. When Tris goes to talk to Tori about her divergence Bud is drawing a tattoo of a lion on another man's arm.
Bud is one of the older Dauntless members who volunteers to guard Jack Kang in his appointment with Jeanine Matthews. He offers himself to guard, to eavesdrop on the conversation and take information back to the rest of the loyal Dauntless members.
Bud is also the first one to suggest Eric's execution before leaving Candor headquarters.
When they get back to Dauntless headquarters after escaping Candor, Bud hands out paintball guns so that the rest of the loyal Dauntless can fire at the hidden cameras. He tells Zeke and Tris to shoot at the cameras near the Pire.
It is unknown if, during the attack of Erudite to Candor, Bud was shot with a transmitter. Hence, it is unknown if he was part of the simulation-ready Loyal Dauntless that attacked the factionless later on. His fate is unknown, but it is presumed he is alive.
Bud is one of the older Dauntless, not old enough to be send with the factionless, though. It is presumed that, since he works at the tattoo parlor, he might also have a couple of tattoos himself.
Bud is the type of person who is curious to know what's happening. Tori mentions once, that she couldn't talk to Tris in such an open place for a long time, since Bud would start asking questions.
He also volunteers to eavesdrop on Jack Kang and Max, which infers his curiosity to know about the topic in discussion.
He and tori worked together at the tattoo parlor for at least a year. He was standing next to Tori when they voted for the new Dauntless leaders.
"We need to decide what to do about Eric. To let him stay here, or to execute him."