Riva is no scholar, critic or cinemaniac. She’s a storyteller, which is why she seems able to record long conversations that took place before she was born, or in places she wasn’t. This is disconcerting at first until you get the idea: when you set out in search of lost time, you ride on the twin engines of imagination and memory. Is Riva making some of this up? Details, details. The book has narrative drive and emotional force. It comes from Riva’s wounded heart, a heart that had to wait until her mother, that sacred monster, at last went ungently into her good night at the age of 90.

Bach, a former movie executive who wrote “Final Cut,” a riveting account of Michael Cimino’s fiasco, “Heaven’s Gate,” is a fan but a learned and analytical one. He adores Dietrich, but he presents all phases of her life with balance and in detail that’s overwhelming only if you think no movie star is worth such massive attention.

Riva’s book will become a best seller because of all that rich, bubbly gossip, not because of its biographical details, which are better orchestrated by Bach. He tells you more about Josef von Sternberg, the Viennese-American Pygmalion who kneaded the young Dietrich into, not a star, but a one-woman galaxy. He tells you about Dietrich’s love for Rilke’s poetry, about the place of the Bauhaus in the cultural ferment of the pre-Hitler Weimar Republic. He’s good on the theme of Dietrich’s bisexuality, but he doesn’t tell you that the divine androgyne went to bed with Colette and with Gertrude Stein. He wasn’t there, but Riva was. Well, in the next room at least, a little girl waiting dutifully for Mutti to do whatever her queen mother did in all those next rooms. “Colette was-wonderful!” beams Dietrich. We don’t find out whether Stein was wonderful, but Riva recalls she was built like a truck with the head of a bulldog.

Riva tells us that after she was born Dietrich gave up sex with her husband, Rudolf Sieber. Dietrich and Rudi stayed married for 53 years until his death in 1976, but his chief conjugal role during that half century was to advise Dietrich on how to conduct her innumerable affairs. The 790 pages can barely contain this roster, which Bach calls the Alumni Association (males) and the Sewing Circle (females). Among the seamstresses was Mercedes de Acosta, who was also Garbo’s lover. Among the alumni were Jean Gabin (“The most beautiful hips I have seen on a man,” said Dietrich), Frank Sinatra (“The only really tender man I have ever known”), Joe DiMaggio (“A little dumb-but sweet!”) Edward R. Murrow (“He smokes even during–you know what I mean”), Adlai Stevenson (“I had to say yes when he asked for ‘it’”), JFK, Yul Brynner and Edward VIII before he abdicated.

This frenetic activity was, says Riva, “emotional gluttony.” Dietrich didn’t really want sex (she said she preferred impotent men) but “declarations of utter devotion.” Riva makes the shocking claim that she was raped by a lesbian nanny hired by her mother. “Why had my mother chosen that woman? Did she want it to happen to me?” Bach of course doesn’t know of this incident, but he says that “Maria had seen too much through too-young eyes.” The mother’s self-absorption and narcissism led to the daughter’s alcoholism and addiction, which ended only when she met and married William Riva, a professor of set design.

Despite the sensationalism, Riva’s testament has a tormented complexity: she cavils at the medals Dietrich won for entertaining troops during World War II, saying that the war gave her the best role of her career. And, recounting Dietrich’s astonishing 20-year gig of concert performances, Riva says these shows provided the perfect lover She had always wanted-the live audience. For Bach these shows were her final triumph as an artist. The last part of Riva’s book is a horrifically powerful evocation of Dietrich holed up in her Paris apartment, bedbound, popping pills, belting booze, exuding an odor of decay. After she died last year, Riva says: “How small she is-this power that controlled my life.” Her book is an exorcism of that power.