Hartbourne (whose first name we never learn) is one of Bradley Pearson's friends and former coworkers from his years as a tax inspector. Bradley describes him as being "a typical denizen of my great years of dullness" (Bradley Pearson's Foreword: par. 8), and, throughout the novel, he uses Hartbourne as an exemplification and representative of the kind of people that Bradley used to hang around with.
Hartbourne spends most of the novel doggedly trying to set up a lunch date with Bradley. He even goes so far as to plan a party in Bradley's honor (which Bradley forgets about, and misses), just so that he can spend some time with his old friend.
When Bradley is put on trial for the murder of Arnold Baffin, Hartbourne works harder than any other witness to convince the judge and jury that Bradley is insane. If that doesn't seem very nice of him, consider that it's a lot more generous than trying to depict Bradley as a vicious, jealous monster, which is what other people do. Although Hartbourne isn't successful, one good thing does come to him out of the trial—he meets Christian Evandale, Bradley's former wife, and marries her soon after.