Bob Wheeler and his wife, June, first appeared in the two-part episode "The Wheels of Fortune", along with their daughter Carolynn. Because a tornado leveled the diner where Bob washed dishes at and destroyed the trailer park where their camper was parked, the Wheelers became homeless. Bob interjects that they found one of the axels on top of a laundrymat in the next country. The family decided to relocate to Florida where they were mugged, loosing everything. They were found on a park bench, crying, and were arrested for vagrancy. When brought into court, Bob explains that they can "take [them] right to the gas chambers, [they] don't care!" Carolynn asks her father if she's ever going to see DisneyWorld. Bob gravely replies that she's never going to see it, "never in a million years".
The couple return (without Carolynn, whose absence is unexplained) in the two-part episode "The Hurricane", where their hot dog stand have been blown away by a tornado. Originally thought to be from West Virginia, they now admit that they've been lying. They're actually Yugoslavian, and apparently Bob picked West Virginia because it was the "first exotic thing that popped into [his] head". In the same episode we learn that both Bob and June speak Spanish. June is Guatamalan on her mother's side and Bob picked up the language on his sabbatical in Madrid. As a result of being trapped in the building, with the hurricane raging outside, the couple help with the birth of a set of quadruplets. One of the children is named Gumo, at Bob's suggestion. Bob explains that it is his grandmother's nickname.
The Wheelers (yet again without Carolynn) return for a third and final appearance in the four-part episode "Her Honor", although they're present in only two of these.
In the first part we find out that they were arrested on a 509B violation; the illegal detonation of poultry. They were trying out egg farming, but a propane powered incubator proved to cause trouble. Bob recals the nightmare; the godawful smell of marengs and blood curdling peeping. June says they initially tried out worm farming, and Bob adds that a stampede put an end to that. Bob is depressed by their failure, and June remarks that he's been "such a downer" since his grandmother died. Bob informs that his grandmother died in her sleep. She was sleeping peacefully on the railroad track. When Harry rules they have to pay the damages, a total of 85 dollars, Christine Sullivan express doubt they can pay that much. June, who's been holding a coffee can for the entire session, pats the lid and says that "Granny did leave [them] a pretty substantial inheritance". Dan Fielding skeptically suggest the coffee can to contain a dead rat and a pack of neco wafers. Bob dismisses him and says that it actually contains 250.000 dollars. June opens the can to reveal the money and Bob admits that they ate the neco wafers.
In the second part, Bull is bying a candy bar, and Bob steps out behind the desk of the newsstand. It turns out that the Wheeler couple bought the stand for their 250.000 bucks, and Bob reveals that they can "hardly believe it [them]selves". Then they charge over 900 dollars for the candy bar, Bull stating that they've gone up in price since last time.