Bagshaw graduated from Washington in 1907 after becoming the first of two five-year lettermen in Washington history. Between 1903 and 1907 Bagshaw played end, halfback and quarterback for Washington under three different coaches. After graduation Bagshaw went to Everett High School where he was head coach from 1909 to 1920. His last Everett squads won consecutive national championships in 1919 and 1920. He was then hired as Washington's head coach in 1921. In his nine seasons at Washington, Bagshaw compiled a 63-22-6 record and took the Huskies to their first ever Rose Bowl in 1924 where they tied Navy 14-14. Bagshaw returned to the Rose Bowl in 1926 where the Huskies lost to Alabama 20-19. Bagshaw retired after the 1929 season and died of a heart attack October 3, 1930 at the age of 46. He was inducted into the Husky Hall of Fame in 1980.