THE LATE ENGLISH NOVELIST Beryl Bainbridge was a favorite among writers. That’s a lovely honor but not quite a ticket to popular success. Bainbridge had two distinct periods. In the first she wrote about young women and the trials of their working lives and the men they never quite understood and who never quite understood them. Those books often open as conventional comedies before they turn black. When Bainbridge was finished mining her own early years, she began her second period with a series of historical novels that brought her additional acclaim in both the United Kingdom and the United States. Her novel of the doomed Scott expedition to Antarctica, The Birthday Boys, was the first of her books to find a significant audience in America.

Her final novel, The Girl in the Polka-Dot Dress, unfinished at the time of her death and published posthumously, is an enigmatic book about a journey starting in Baltimore and ending up in Los Angeles at the Ambassador Hotel in time for Robert Kennedy’s death. Following the actual murder, the Los Angeles Times reported that “a girl in a white polka-dot dress ran from the hotel … and said, ‘We shot him.’” Then she disappeared into the mysteries of American assassination lore. Bainbridge has imagined her back into the half-life of fiction.

Road novels are an American habit. A few of them, On the Road and Lolita, seem indelible. It’s a big country, and a car, or in this case, a camper, is a good way to see it. Rose, the young protagonist, is a London dental assistant traveling across America in the era of murders searching for a Dr. Wheeler, an American who was kind to her in earlier days. She’s traveling with one Harold Grosse, known as Washington Harold, an American who is also looking for the doctor, but for his own purposes: Dr. Wheeler may have had an affair with Harold’s late wife. Harold is carrying a pistol.

Rose and Harold’s true purposes remain private and vaguely stated, though the elusive Dr. Wheeler may have a connection to the Kennedy organization. Harold, Bainbridge tells us, has “a soul immersed in darkness.” Rose is younger, unobservant and a little dim, though she can be devious.

The book brings together both of Bainbridge’s modes: The journey itself, with its promise of comedy and misunderstandings that tend toward darkness, recall her earlier works, while the assassination’s palpable historicity reflects her later period. The trip includes various eccentric stops: a Theosophist meeting, a funeral, a campsite—all surrounded by a lot of confusion and a touch of dreary sex. Bainbridge concocts people who can be self-absorbed and often annoying but are rarely aware of their effect on others. It’s true of Rose and many of Bainbridge’s other women. As for Rose and Harold, Bainbridge keeps pulling us along without revealing their secrets, though one suspects they’re going to enter history. If the novel loses its way in the climactic scenes at the Ambassador Hotel...