He was at Candor headquarters during the attack by the Dauntless traitors. Due to the fact that he was Divergent the simulation gas released during the attack did not cause him to fall unconscious, Eric and all of the other traitors captured him along with the other Divergents, including Tris Prior and Uriah Pedrad.
Bobby was described by Tris as being quite a brave boy because he was said to not seem afraid of the Dauntless traitors because he was staring at them directly. The point of the invasion was to find out who was Divergent so they could bring a couple of them to Erudite Headquarters to do testing on them. After explaining that a young Divergents' brain was nowhere near finished developing, Eric shot Bobby, as he was useless to Jeanine Matthews.
Later, when the loyal Dauntless are about to execute Eric, murdering Bobby is cited as one of the crimes he is being punished for.
Due to the fact that Bobby was not a main character and had a short appearance in Insurgent, not much is known about his physical appearance. He was described by Tris as a young boy, around eleven years old.