Åsheim, who started for the Tromsø skiklubb, ran her first race in the Continental Cup in Gaasbu in December 2002 , finishing 30th in the sprint. She made her World Cup debut in March 2003 in Oslo , which she finished in 43rd place in the sprint. In the 2007/08 season she reached the Scandinavian Cup with five top ten placements, including second place in the sprint in Riga , fifth place in the overall standings. In March 2008 she got her only World Cup points with 21st place in the sprint in Drammen . In her last active season, 2008/09, she came seven times in the Scandinavian Cup in the top ten, including third place in the sprint in Ulricehamn and finished third in the overall standings. She completed her 15th and last World Cup race in March 2009 in Oslo, which she ended prematurely.