Bicket was educated at Radley College, Christ Church, Oxford, where he was an organ scholar, and the Royal College of Music. Before Oxford, he was an organ scholar at St George's Chapel, Windsor. Afterwards, he was sub-organist at Westminster Abbey, during which time he performed at the wedding of Sarah Ferguson and Prince Andrew.
As a conductor, Bicket became known when he stood in as a replacement to conduct Peter Sellars' production of Handel's opera Theodora with Dawn Upshaw, Lorraine Hunt Lieberson and David Daniels, at the Glyndebourne Festival in 1996. In 2003, Bicket made his Covent Garden debut conducting Handel's Orlando with the Orchestra of the Age of Enlightenment (OAE). In 2004, Bicket made his first appearance at the Metropolitan Opera in a production of Rodelinda with Renée Fleming in the title role.
In October 2006, Bicket was named music director of The English Concert, and formally assumed the post in September 2007, his first orchestral directorship. He first worked with The English Concert as a harpsichordist in 1984. Bicket has conducted commercial recordings with The English Concert for harmonia mundi.
Bicket first conducted at Santa Fe Opera (SFO) in 2004, in a production of Agrippina. He returned to SFO as conductor for subsequent productions of Platée (2007) and Radamisto (2008). In April 2013, SFO named Bicket its next chief conductor, effective 1 October 2013. Although the formal press release did not indicate a specific time length of Bicket's initial contract, SFO general director Charles MacKay stated an informal duration of 4–5 years. In November 2016, Santa Fe Opera announced the extension of Bicket's contract as chief conductor through 30 September 2020.
- Andrew Clements (2003-10-08). "Orlando (Royal Opera House, London)". The Guardian. Retrieved 2007-04-07.
- Anthony Tommasini (2004-12-04). "Handel Discovers Big Home At the Met". The New York Times. Retrieved 2013-05-01.
- Tim Ashley (2011-03-10). "Bach: Cantatas and Arias – review". The Guardian. Retrieved 2013-05-01.
- "Chief Conductor Announced" (Press release). Santa Fe Opera. 25 April 2013. Retrieved 2013-05-01.
- Anne Constable (2013-04-24). "Harry Bicket named new chief conductor of Santa Fe Opera". Santa Fe New Mexican. Retrieved 2013-05-01.
- "Santa Fe Opera 2016 Season in Review" (PDF) (Press release). Santa Fe Opera. 17 November 2016. Retrieved 2016-12-27.
- Anthony Holden (2004-10-09). "Handel, Arias". The Observer. Retrieved 2007-04-07.
- Edward Greenfield (2004-11-11). "Handel: Arias from Semele, Scipione, Orlando, Giulio Cesare, Lotario, Alexander Balus, etc, Fleming/ OAE/ Bicket". The Guardian. Retrieved 2007-04-07.
- Anthony Holden (2004-05-29). "Handel: Arias, Lorraine Hunt Lieberson". The Observer. Retrieved 2007-04-07.
- Tim Ashley (2007-08-09). "Handel: Arias; Bostridge/ OAE/ Bicket". The Guardian. Retrieved 2013-05-01.
- Askonas Holt agency biography of Harry Bicket
- Stephen Clarke, 'Becoming Conductors', Lusimus: The Radley Newsletter Issue 8 (January 2004)
|Music Director, The English Concert
|Chief Conductor, Santa Fe Opera