Bousfield was born in York, England and began playing the trombone at the age of seven, taught by his father. He became principal trombonist in the National Youth Brass Band at age 13, and for four years, principal with the Yorkshire Imperial Band, during which time they won the British, National and Yorkshire championships.
In 1979, Bousfield became the youngest winner ever of the Shell/London Symphony Orchestra Music Scholarship.
In 1980 Bousfield joined the European Union Youth Orchestra where he spent two years under Claudio Abbado. He spent only six months studying at the Guildhall School of Music and Drama before he was appointed Principal Trombone at the Hallé Orchestra in March 1983.
In 1988 at the age of 24, Bousfield was appointed principal trombonist of the London Symphony Orchestra, taking over from the veteran Denis Wick. At the time, Denis Wick said, "he is an extremely accomplished player and what he is short on by way of experience, if he is, he is bright enough to get together very quickly."
Ian was appointed professor of trombone at the Royal Academy of Music in 1992 and has since been awarded Honorary Membership of the Royal Academy of Music.
In September 2000 he accepted a new position as principal trombonist of the Vienna State Opera/Vienna Philharmonic, on an equal footing with Dietmar Küblböck.
In September 2008, Bousfield performed the Nino Rota's trombone concerto with the Vienna Philharmonic in the Lucerne Festival conducted by Riccardo Muti.
In March 2007 Bousfield gave the premiere of Stargazer, a concerto for trombone and orchestra by British composer Jonathan Dove. The performance was with the London Symphony Orchestra conducted by Michael Tilson Thomas.
In 1984 he performed Elgar Howarth's trombone concerto with the Yorkshire Imperial Band for broadcast on BBC Radio 3. And in 1985 he played the first British performance of Gunther Schuller's trombone concerto, Eine kleine Posaunenmusik with the Halle Orchestra conducted by the composer.
Bousfield's solo recordings started with a mix of popular solos with brass band and synthesizer in "The Versatile Virtuoso" (1992, Doyen DOY CD014) where he is accompanied by his former band, the Yorkshire Imperial Band. This was followed by Frank Martin's Ballade with the London Philharmonic Orchestra and Matthias Bamert (Chandos), Elgar Howarth's concerto for trombone with Eikanger-Bjørsvik Musikklag and Howarth conducting (Doyen), Derek Bourgeois' trombone concerto with the Sun Life Band, much of the standard trombone and piano repertoire on EMI as part of its Virtuosi series and most recently the Bourgeois' trombone sonata with the YBS Band and David King.
In October 2006, Bousfield released the CD "Pryor Engagement" (Doyen DOY CD212). This recording contains solos composed by, or famously performed by, the legendary American trombonist Arthur Pryor. Accompaniment is provided by Black Dyke Band.
In 2007, a further solo CD was released on the Japanese Camerata label (CM28117). The CD is called Solo Trombone - French Collection and includes classical repertoire for trombone and piano.
His orchestral recordings are numerous, but the highlights include the "Star Wars Episode I: Phantom Menace" recording with the LSO (BMG, 1997), the tenor horn solo in Mahler's 7th Symphony with Michael Tilson Thomas and the LSO (Sony, 1999), the large trombone solo in Mahler's 3rd Symphony with Pierre Boulez and the VPO (DG, 2003), and with the same forces, the live Mahler 2nd symphony, particularly the final movement.
Also notable are his recordings with the LSO Brass, particularly "American Brass".