His father was musical, and sang himself; when his son developed a fine treble voice, he decided to bring him up as a musician.
Benjamin Cooke, the organist of Westminster Abbey, turned down young Busby (at age 12-13) as too old for a chorister; he was placed under Samuel Champness for singing, and Charles Knyvett for the harpsichord.
He then turned his attention to oratorio, and began a setting of Alexander Pope's Messiah, at which he worked intermittently for several years.
In 1785 he wrote a poem called The Age of Genius, a satire in the style of Charles Churchill, containing nearly 1,000 lines.
[2] In the spring of 1799, his early oratorio was produced by Wilhelm Cramer under the name of The Prophecy, perhaps to avoid comparison with Georg Handel's Messiah.
A secular "oratorio", Britannia (words by John Gretton), was sung at Covent Garden in 1801 with Gertrud Elisabeth Mara as the principal soprano.
Busby also wrote music for Richard Cumberland's version of Kotzebue's Joanna, which was produced at Covent Garden on 16 January 1800, without much success.
[3] His exercise on this occasion was "A Thanksgiving Ode on the Naval Victories", the words of which were written by Mrs Crespigny.
In 1802 he wrote music to Thomas Holcroft's melodrama A Tale of Mystery, the first play of this type that appeared on the English stage.
[2] In his latter years Busby lived with a married daughter at Queen's Row, Pentonville, where he died, aged 84, on Monday, 28 May 1838.