Bowman's background is in Anglican church music. He was educated at The King's School, Ely, and began singing as a boy chorister at Ely Cathedral. He later went to New College, Oxford. He was a member of the New College and Christ Church choirs.
In 1967, while still a student, he auditioned for Benjamin Britten's English Opera Group. He was cast as Oberon in A Midsummer Night's Dream, a part which had been composed with Alfred Deller's voice in mind: Bowman, who had a larger voice than Deller, went to have a long association with the part. He appeared at Glyndebourne in 1970 in Francesco Cavalli's La Calisto (the first countertenor to sing there), at English National Opera in 1971 in Semele, and at the Royal Opera House, Covent Garden in 1972 in Taverner. In 1973 he created the role of the "Voice of Apollo" in Britten's Death in Venice.
Bowman retired from the operatic stage to concentrate on concert work after having appeared at most of the world's major opera houses including La Scala, Milan; Amsterdam, Paris, Aix-en-Provence, Sydney, Verona, Vienna, Strasbourg, Sante Fe, Dallas, and San Francisco.
In 1967 Bowman made his London debut at the opening concert of the Queen Elizabeth Hall.
In... Bowman met David Munrow and was invited to join the Early Music Consort of London. The ensemble flourished in the ten years 1967–1976, making numerous recordings and touring extensively. After Munrow's death in 1976, the consort disbanded but Bowman continued to work with former members such as the harpsichordist and conductor Christopher Hogwood and the lutenist Robert Spencer. During the late 1960s Bowman sang regularly with the choir of Westminster Abbey.
For many years Bowman was a member of the early music choral group Pro Cantione Antiqua.
As well as the association with Britten mentioned above, he has given the world premieres of contemporary compositions by composers such as Geoffrey Burgon, Alan Ridout and Richard Rodney Bennett. He also commissioned the Self-laudatory hymn of Inanna and her omnipotence from Michael Nyman.
In recital he works frequently with the lutenist Dorothy Linell and the pianist Andrew Plant.In 1992 the French Government honoured him with admission to L'ordre des Arts et des Lettres and he was also awarded the Medal of Honour of the City of Paris, in recognition of his long-standing contribution to the musical life of that city.
Bowman is also President of the Holst Singers.
In May 1992 Bowman received the Honorary Degree of Doctor of Music from the University of Newcastle upon Tyne.
He was made a CBE in the Queen's Birthday Honours in June 1997.
In November 1998 Bowman was made an Honorary Fellow of New College, Oxford.
In December 2006, following the death of Sir Malcolm Arnold, Bowman was installed as Patron of the Northamptonshire Choral Foundation, and thus the Choirs of All Saints' Church, Northampton.
Bowman has made over 180 recordings with all the major record labels and has also worked with many leading conductors including Nikolaus Harnoncourt, Frans Brüggen, Christopher Hogwood, John Eliot Gardiner, Roger Norrington, and Gustav Leonhardt. Between 1988 and 2001 he made many recordings for Hyperion Records with The King's Consort and their conductor Robert King, including the complete Purcell odes, secular songs and church music, Handel Judas Maccabaeus, the Occasional Oratorio, Deborah, Joseph and his Brethren, Ottone, and Joshua, discs of Schelle, Kuhnau and Knüpfer, and two solo discs of Handel arias. Twentieth-century repertoire includes Vaughan Williams' Ten Blake Songs and "Linden Lea", on the Meridian Records label (CDE 84158).Songs of Innocence, recital album with Andrew Swait (treble) and pianist Andrew Plant, Signum 2007