After her uncle Jimmy Burgess introduced her to the recordings of Dizzy Gillespie and Miles Davis, she caught the jazz bug and purchased records by Al Hibbler, a vocalist who had a big influence on her singing style. When she was ten she performed at Harlem's Apollo Theater, and despite the enthusiastic reception she received in front of one of the world's toughest audiences, her mother refused to let her go on the road with her uncle, a trumpet player. Shaw attended the State Teachers' College in Potsdam, New York, but later dropped out. For some time in 1963 she worked around New England with a trio led by Howard McGhee.
By the mid-'60s she was performing regularly for audiences in the Catskills, Playboy Clubs, and other New York area venues. In 1966, she recorded "Mercy, Mercy, Mercy" for Cadet Records, and the single sold very well for an unknown singer. The success of the single, a rare vocal version of the tune, prompted executives at Cadet to encourage her to record a whole album for the label in 1967. The diversity of styles, including blues, jazz, and pop standards, was reflected in the album's title, Out of Different Bags. Through her accountant, she was brought to the attention of bandleader Count Basie, and she ended up singing with the Basie band for four years.
In 1972, after leaving the Basie Orchestra, Shaw was the first female vocalist signed to Blue Note Records, and she toured for a while with the Sammy Davis, Jr. She recorded five albums and several singles for Blue Note, and critics likened her singing style to Dinah Washington and Sarah Vaughan. At her club shows, Shaw dazzled audiences with her intoxicating blend of straight-ahead jazz, soul, pop, and classic R&B, but her recordings also satisfied those fans of traditional jazz who had no prejudices about blues and R&B. In 2014, Blue Note Records (Europe) began reissuing her catalog titles, and in 2017 Akshin Alizadeh delivered two remixes of her signature "Woman of the Ghetto" track as a limited-edition single on Cold Busted. The recording was spun by Gilles Peterson and made club DJ playlists across Europe, Asia, and the United States. ~ Richard Skelly, Rovi