Although he is but a supporting player in The Sun Also Rises, Bill Gorton serves many purposes in the novel. As such, he exemplifies Hemingway's command of the storytelling craft, even at the dawn of the author's career.
First, Bill provides much-needed comic relief in a story that is otherwise unremittingly grim, if fascinating. Granted, many of Bill's jokes, especially on the Burguete fishing trip, have not outlasted their particular time; his topical humor is as dated to us as that of Shakespeare or Chaucer. Bill's drunken babble upon his return to Paris from Vienna is eternally comical, however. Ditto his inebriated quest for a stuffed dog.
Secondly, Bill's presence in the novel allows Hemingway the opportunity for more characterization of his protagonist. Jake says things to Bill that he says to no one else — not even the reader. We learn via their friendship that Jake is capable of generosity and warmth toward another man (as opposed to his competitive behavior with Cohn). And Bill shows us how Jake appears on the outside, to those who (unlike the reader) aren't privy to his inner torment. Bill is Jake's public face.
Unlike Jake, Brett, Mike, and the Count, Bill Gorton did not fight in a war, though a comment about his presence in Paris just after the armistice indicates he may have been a war correspondent. And yet not only Jake, but Brett and Mike as well, accept him as a peer while rejecting Cohn. Is Bill gay? He's practically the only male character indifferent to Brett's charms, the spell she casts over men of every age and nationality. Perhaps, like Jake, Bill has struggled with a sexual secret. Carrying the burden of his sexuality in a homophobic culture might be a battle that Bill fights every day — one that allows him to fit in with the group in a way that Robert Cohn can't.