Writing in reaction, she says, to recent stories in ""national tabloids"" about her longtime affair with Humphrey Bogart, Thompson now tells her own story--which will be serialized in the Star, a national tabloid. And though Thompson wants to be remembered as more than just ""a sleazy footnote in Bogie's history,"" this sleazy-but-dull memoir won't help any. The affair began when Bogie was going through rotten times with alcoholic wife #3 Mayo Methot (whom Bogie did originally love, says Thompson) circa 1942; Verita, also married unhappily, was a film studio hairdresser/wigmaker. (""You've got a great ass, ol' girl,"" said HB at their first meeting.) But even with both their divorces in the works, Verita declined Bogie's marriage proposal (she says), taking a wait-and-see approach--so Bogie promptly married Lauren Bacall. End of affair? No sirree. Bogie, according to Verita, immediately regretted the wedding (Bacall was ""a pretentious, opportunistic interloper""), saying: ""Any chance that we might pick up where we left off, Pete? . . . I can't get you out of my mind."" And Verita, though courted over the next years by husband-to-be Waiter Thompson, became Bogie's secretary/traveling-companion through the next decade. The bulk of this book, then, is devoted to bland, dreary anecdotes from Thompson's travels with Bogie: his press confererences, his fondness for ""ribs"" (put-ons of friends), etc.--with mild guest appearances by Ava Gardner, William Holden, and others. But even movie buffs will find this thin, pulped-out stuff--not terribly sordid, just vaguely pathetic, with no new insights into Bogart as personality or actor.