“This is the first time I ever ate a bagel!” Ginger Rogers exclaimed as she smeared the cheese. Alexis Smith, Ruth Warrick, Sylvia Miles, Lenny Baker, Rex Reed and other admirers joined her for brunch on March 7, 1976, at Prive, the chic East Side restaurant. After an absence of many years from New York — she was last seen in Hello, Dolly! here — she opened a singing and dancing engagement at the Empire Room of the Waldorf-Astoria.