On December 30, 1980, Bøgseth jumped in Oberstdorf, his first jumping in the ski jumping world cup . In the first two competitions as part of the Four Hills Tournament 1980/81 , however, he could not win any World Cup points. It was only in his third World Cup on the Copper Peak ski jump in Ironwood that he made it into the points with 9th place. Also in the second competition he was able to win two World Cup points with 13th place. A week later he achieved a further improvement in Thunder Bay, Canada, with 6th place, before he was on the podium for the first time in Chamonix with 2nd place. After he was able to achieve a 4th place in Saint-Nizier in France and a 10th place in Planica , he finished the 1980/81 World Cup season in 15th place in the overall standings. At the Norwegian Championship in Eidsvoll, which took place shortly afterwards, he won the silver medal on the normal hill behind Ivar Mobekk . In the following season he did not take part in any World Cup jumping. In the 1982/83 season he was placed in the top twenty in all World Cup competitions, four times even in the top ten. In the end, he finished 19th in the overall World Cup ranking and then ended his active ski jumping career.