Poirot, as a result of spreading fame, has been overworked and Captain Hastings suggests he rests by accompanying him on a week's holiday to the south Devon coastal resort of Ebermouth. On their fourth day there, Poirot receives a note from the theatrical agent Joseph Aarons who asks him to travel to Charlock Bay on the north Devon coast as he needs to consult him on a matter. The two are planning to go by train but Captain Hastings sees a notice for a motor bus tour from the one resort to the other which will save time on changing trains. Poirot reluctantly agrees, afraid of the uncertain English climate and the drafts of air which will invade the bus. They book their tickets at the office of the company concerned where Captain Hastings is taken with another customer, an auburn-haired girl, whereas Poirot is intrigued by a young man who is attempting to grow a feeble moustache.
The next day on the bus the two find themselves sat with the young girl who introduces herself as Mary Durrant. Her aunt is in Ebermouth and runs an antiques shop where she has managed to make something of a success for herself. Mary has started to work with her aunt as opposed to becoming a governess or a companion and she is travelling to Charlock Bay to take a valuable set of miniatures to an American collector there by the name of J. Baker Wood for perusal and purchase.
The bus stops for lunch at Monkhampton and Mary Durrant joins Poirot and Captain Hastings at a table in a café. Part way through their conversation, she rushes outside and returns saying that she thought she saw through the window a man taking her suitcase with the miniatures off the bus, when she confronted him she realised his case was almost exactly like hers and that she was in error. She does however describe the young man that Poirot and Hastings saw the previous day in the booking office.
The bus arrives in Charlock Bay and both Poirot and Hastings and Miss Durrant book into the Anchor Hotel. They have barely started unpacking when a white-faced Miss Durrant appears and tells them that her suitcase has been unlocked somehow, the despatch case inside containing the miniatures has been forced open and the items stolen. Having heard that Poirot is a detective, she asks him to investigate. Poirot telephones Mr. Wood who tells him that he had a visit half-an-hour ago from someone representing themselves as calling on behalf of Elizabeth Penn, Mary Durrant's aunt, and he paid her five hundred pounds for the miniatures.
Poirot and Hastings go to visit Mr. Wood, Poirot voicing his puzzlement over why the thief took the time to force the lock of despatch case while leaving it in the suitcase instead of taking the inner case away with them and opening it at their leisure.
The two meet Mr. Wood and take an instant dislike to the brash, vulgar man. He gives them a description of the seller: "a tall woman, middle-aged, grey hair, blotchy complexion and a budding moustache". Poirot finds out that the young man on the bus, Norton Kane, has an alibi for the period in question.
The next day, having sorted out Joseph Aaron's problem, Poirot and Hastings return to Ebermouth but, at Poirot's insistence, this time by train. They call at Elizabeth Penn's shop and Poirot almost immediately accuses the elderly lady of being Mr. Wood's visitor of the previous day in disguise and meaningfully tells the two women their scam must cease. Miss Penn, white-faced, agrees.
Poirot points out to Hastings again the absurdity of the despatch case being forced but left in the suitcase. When they were booking their tickets on the excursion, he saw Miss Durrant watching Mr. Kane and wondered why she was so interested. He expected something to happen on the trip and it did. Mr. Wood would have had to return the miniatures as they were officially stolen goods and the two women would have had his five hundred pounds and still possessed the miniatures to sell on again. Their plan was to pass suspicion on to Mr. Kane and have Poirot and Hastings as two duped witnesses.