He has been a soloist with orchestras in Pittsburg, Cleveland, Los Angeles, Melbourne, Sydney, Cologne and New York. He gave the Australian premiere of Michael Colgrass' "Chaconne" for viola and orchestra, which was broadcast on ABC Radio.
Doctor Bucknell has given recitals in Sweden, France, Germany, Italy, New Zealand, Canada, America and Australia and has performed in London's Wigmore Hall, France's Grange de Meslay, Radio France and in many other European halls. While in Europe, he was loaned the "Mahler Stradivarius" which was the first Viola Stradivarius made.
As a chamber musician, he has won prizes including the Interpretation Prize in the Osaka Competition in 1996 and the Audience Prize in the Melbourne Chamber Strings Competition. He was the violist of Belgian String Quartet "Quatuor Danel" which won prizes at the Evian, London and Moscow Quartet Competitions