Chapter 6, entitled Endless Summer is the last chapter of Bully.
PlotEditIt is the summertime, although classes remain in session. Jimmy has brought relative peace to the school, and has 100% respect with all six of the cliques. Since there are no further story-related missions, this chapter, as implied by the title, does not end.
Chapter 6 is a free-roam chapter in which Jimmy can finish up any non-storyline missions he has yet to complete, collect items, win races, finish up classes, play games, or do any number of the things he hasn't already done. Since he has 100% respect from everyone, there is no fighting to worry about unless Jimmy chooses to initiate it.