Bremseth, who started for the Hokksund IL club , made his international debut on December 30, 1979 at the first competition of the newly created Ski Jumping World Cup in Oberstdorf . However, he could not achieve a top placement in this jumping or in the other three of the Four Hills Tournament 1979/80 . After a year break, Bremseth came back to the World Cup in Sapporo in February 1981 and immediately impressed with his first podium finish in second behind Armin Kogler . He also reached this position in the second competition, this time behind Hans Wallner . However, it was his last podium finish for a year.
At the Nordic World Ski Championships in Oslo in 1982 , Bremseth won bronze in the individual on the normal hill and together with Johan Sætre , Per Bergerud and Olav Hansson won gold in the team competition on the large hill. In March 1982, Bremseth won all jumping competitions, except the ski flying competitions in Planica . In the end, he reached fifth place in the overall World Cup.
In the 1982/83 season he could no longer build on the performance and therefore withdrew from the World Cup in March 1983 for the time being. In January 1986, Bremseth came back to a World Cup start in Oberwiesenthal . With a ninth place, he finally said goodbye to professional sport.