Bjerke, who had won bronze at the Junior World Championships in 2000 in Štrbské Pleso, Slovakia, with the Norwegian relay team and was sixth in the individual race over 30 kilometers, made his debut in the Continental Cup in Orsa in December 2000 . In this series he took second place in the pursuit race in Fiemme Valley in February 2002, third place over 10 km classic in December 2014 in Gåsbu and again third place over 15 km freestyle in Hommelvik in February 2004 three podium finishes. Bjerke achieved another top 3 result over 15 km classic at the Scandinavian Cup in Keuruu in January 2009 with second place.
In the World Cup started Bjerke first time in March 2001 in Oslo , where he was ranked 20 km classic on the 50th He achieved his best individual result in the World Cup in January 2005 in Otepää with fourth place over 15 km classic. In addition, Bjerke reached seventh place in Falun in March 2003 and sixth two years later at the same place with Norwegian relays two more top 10 results.
With the relay Bjerke was a total of three times Norwegian champion and also won the national championship title in the team sprint in 2005. Bjerke started in the skiathlon at the Nordic World Ski Championships in Oberstdorf in 2005 and finished the race in 25th place.
Bjerke finished tenth in the Birkebeinerrennet in 2008, fifth in 2011 and third in 2012 and 2013.