Indecisive heiress Dee Dee Dillwood is pushed into marrying her sixth fiancTe, but unable to face the wedding night, she flees into the adjacent hotel room of commercial pilot Marvin Payne, who just wants to sleep. Somehow, she persuades him to take her to California. Her fellow passengers include a chimpanzee, a corpse (in a coffin), an absconding embezzler, and two smoochy newlyweds. Can love be far behind?

Moments before she is to marry stuffy Henry Benson, New York heiress Diana "Dee Dee" Dillwood complains to her uncle and guardian, Ralph Tutwiler, that she is having second thoughts. Having gone through six previous broken engagements with Dee Dee, Ralph and psychologist Dr. Blucher advise her to stop doubting herself and "plunge into it" with Henry. Dee Dee agrees, but as soon as she and Henry arrive at the Hampshire Hotel to start their honeymoon, she panics. When Dee Dee tells Henry she has made a mistake, Henry declares that he will not be humiliated and lunges for her. Wearing a dressing gown, Dee Dee runs from their room and hides in the neighboring wedding suite, which is being occupied by pilot and airline owner Marvin Payne. Dryly presuming that she is a "lost lamb," Marvin, who is staying at the hotel courtesy of night manager Dick Hebert, agrees to allow Dee Dee to spend the night in the suite. The over-excited Dee Dee, now calling herself Dottie Blucher, then asks the exhausted Marvin for a sleeping pill, and he phones Dick to have one delivered. Dick's suspicions are aroused when he sees that Marvin is sleeping on the couch and searches the suite. Dee Dee has hidden herself, however, and Dick leaves, satisfied that no "hanky-panky" is going on. Early the next morning, Marvin's business partner and co-pilot, Bullets Baker, shows up and finds Dee Dee still knocked out by the pills. Marvin explains the situation, and as they have a scheduled flight to fly, he and Bullets try frantically to wake Dee Dee, but finally are caught by Dick. While Marvin and Dick rouse and dress Dee Dee in some of Marvin's pilot clothes, Bullets stalls a young couple who are due to be married in the suite. Marvin and Bullets then sneak the half-conscious Dee Dee out of the hotel and take her to the Newark, New Jersey airport, from which their twin-engine cargo plane is to fly. There, Dee Dee begs Marvin to fly her out of town, insinuating that she is in a serious predicament. Marvin agrees to take Dee Dee as far as Chicago, then learns that the free-wheeling Bullets sold the newlyweds from the hotel, Georgia and Milton Goodrich, two "tickets" to California for $100. Just before take-off, Dee Dee confesses to Marvin that she sold a man named Mr. Caslon a ticket to California for $300. During the flight, which they share with a cigar-smoking chimpanzee named Joe, Marvin reveals to Dee Dee that he is not going to marry until he has enough money to comfortably support a family, an eventuality he calculates will not occur until 1954. When they land in Chicago, Dee Dee, who is falling for Marvin, reluctantly says goodbye to him, but he gives in and invites her to California. Soon after, a detective asks Marvin and Bullets if they are carrying a blonde who, along with her middle-aged partner, is wanted for embezzlement. Although the pilots answer no, they both conclude that the blonde is Dee Dee, especially after she returns from a shopping trip nicely dressed and bearing gifts. Once back in the air, Marvin questions Dee Dee about her situation, but she is evasive. To Bullets' annoyance, Marvin decides not to land in Kansas City, as planned, but to go on to Tulsa to avoid authorities looking for Dee Dee. Near Tulsa, however, a storm hits and Marvin makes an emergency landing in a farm field. After farmer Matt Racknell and his family invite the crew and passengers to spend the night in their home, Dee Dee and Marvin finally admit their mutual attraction and kiss. A guilt-ridden Caslon then confesses to Marvin that he is the embezzler and that his blonde secretary cajoled him into committing the crime. Now completely confused about Dee Dee, Marvin calls Dick in New York to inquire about her. The next morning, while trying to move the plane out of the muddy field, Marvin snubs Dee Dee without explanation. When Dee Dee finally realizes that he knows about her engagements and marriage, she tries to convince him that she truly loves him, but he rejects her. With the help of some Cherokee Indians, the plane is pulled to dry land and takes off for California, without Dee Dee. As soon as he lands in Burbank, Marvin learns that, because of the unexpected delays and other problems, his airline faces bankruptcy. During an impromptu stockholders meeting, however, Marvin discovers that Dee Dee has bought the company. Furious, Marvin finds Dee Dee at her aunt Martha's Bel Air home and informs her that he is not working for a woman. Dee Dee, who has just arranged for an annulment from Henry and has taken another sleeping pill, tries to argue with Marvin, but falls asleep. The next day at the airport, however, she tells Marvin that he is going to run the company while she has babies, and then presents him with his own four-engine plane.