Son of James Dance and Elizabeth Hooper.
William Dance studied the piano under Theodore Aylward (1730-1801) and the violin under Karl Friedrich Baumgarten (ca. 1740-1824). He played the violin at the Theatre Royal from 1771 to 1774 and in the King's Orchestra from 1775 to 1793, and he was the lead violinist at Haymarket Theatre during the summer seasons from 1784 to 1790, as well as at the Händel commemoration in Westminster Abbey in 1790. He later became a noted teacher of music, and in 1813 was one of the founders of the Royal Philharmonic Society of which he became director and treasurer.
Boswell had obviously met him before when, on October 26, 1762, he visited Mrs Dance and her son. He described him as "a boy of much genius [who] will probably be a man of distinction."