He received a silver medal in quadruple sculls at the 1988 Summer Olympics in Seoul, together with Alf Hansen, Vetle Vinje, and Rolf Thorsen.

[1] He also received a silver medal in quadruple sculls at the 1992 Summer Olympics in Barcelona, together with Kjetil Undset, Per Sætersdal, and Rolf Thorsen.

[3] The crew, which also consisted of Alf Hansen, Vetle Vinje and Rolf Thorsen, also participated at the 1988 Olympics in Seoul.

[6] After the 1992 Olympics, Thorsen and Bjønness turned again to double scull, where they won a silver medal in 1993 World Cup and a gold in 1994.

Bjønness ended his international career after winning the gold medal with Thorsen in the 1995 World Cup.