Born in Strichen, Aberdeenshire, he began his art studies in his twenties after moving to Glasgow. He served an apprenticeship as a
stone carver with the architectural sculptors
Holmes & Jackson
, while attending classes at the GSA
. He later became a
pupil-teacher at the school.
Winning the Keppie Scholarship (donated by the architect John Keppie) in 1932, he travelled to Copenhagen for further study with
Einar Utzon-Frank, the Danish Neo-Classical sculptor.
After returning to Glasgow, he was selected as one of a host of Scottish sculptors to produce statues and groups for the facades
and interiors of the pavilions of the Empire Exhibition, held in Bellahouston Park in 1938.
Bissetís contribution was for the plaster statues of David Livingstone and James Watt on the exterior of the Scottish
Pavilion North, where they stood beside statues of other famous Scots by Scott Sutherland: Robert Burns, Sir Walter Scott and Thomas Carlyle. All the statues were lost when the exhibition site was cleared in 1939.
By this time Bisset had won the Prix de Rome, which enabled him to tour Italy and Greece, where he worked in Athens for the British School of Archaeology. He returned to Britain and became Head of Sculpture at Leeds School of Art and The Guilds School of Art in London.
In the 1960s, he received his second commission for architectural sculpture in Glasgow; a relief panel for the Pathology Department at
the Victoria Infirmary, entitled The Reaper, which depicts a bucolic scene of a man reaping corn with his dog playfully barking at
him. The panel is above the mortuary door and is a joyful contrast to the usual conception of the 'Grim Reaper' (1965).
In 1980, he moved to Mexico for health reasons, then returned to Glasgow, where he specialized in private commissions for bronze busts and nude figures. His work in public collections includes two busts in Kelvingrove Art Gallery, and a plaster bust of William Stewart in the Peopleís Palace, Glasgow.