Ashby's first game was in 1973 with the Cleveland Indians. In 1977 he played the first of two seasons with the Blue Jays; in fact, he was the first player acquired from a trade for the Blue Jays. His longest stint was with Houston, where he played from 1979-89.
Following his career as a player, Ashby worked in broadcasting in Houston; later on he managed in the minor league system. He started with the WhiteWings, followed by the Cobras (a class A Astros farm team). In 1997 he joined the Astros coaching staff. Currently he is on the broadcasting crew for the Blue Jays.
In 2000 he was inducted into the Texas Sports Hall of Fame.