Mr. Bun is the stuffed rabbit belonging to Susie Derkins and who frequents Susie's "tea parties" as a "guest." Unlike Hobbes, Mr. Bun is never seen as anything more than a stuffed rabbit, having no "alternate reality" of his own (at least in Calvin's eyes). In a week-long series revolving around the loss of the stuffed Hobbes, who is found by Susie while out for a walk, Calvin loses the companionship of the alternate Hobbes while the actual stuffed and motionless Hobbes is served tea alongside an equally motionless Mr. Bun. The alternate Hobbes reappears when Calvin finds him sipping tea alongside Susie and Mr. Bun.
Given one of the more unusual aspects of the Calvin and Hobbes universe, namely the fact that the only other children in the strip besides Calvin are Susie and Moe, Mr. Bun may well be Susie's only friend. This is evidenced in a strip from July 29, 1986 which focuses on Susie having a conversation with herself lamenting that she doesn't need Calvin for a friend. The final panel shows a dejected Susie, head in hands, with her final word on the situation: "Poop." Another self-conversational strip from January 13, 1987 witnesses Susie wishing she had a hundred friends with which to ostrasize Calvin, then admitting this is an unrealistic goal for her.
See also: Hobbes' reality