Born in Long Beach, California, Ashby attended San Pedro High School in Los Angeles where he was selected by the Cleveland Indians in the third round of the 1969 Major League Baseball Draft. After spending four seasons in the minor leagues, he made his major league debut with the Indians on July 3, 1973. In his first game, Ashby was a defensive replacement in the ninth inning, as he caught Jerry Johnson for a scoreless inning as the Indians lost 5-4 against the Detroit Tigers. The next day, on July 4, Ashby was in the starting lineup, going 1 for 4 with an RBI in Cleveland's 5-2 win over the Tigers. Ashby collected his first career hit off of Tigers pitcher Mike Strahler in his first career at-bat. On September 29, Ashby hit his first career home run, hitting a two-run home run off of Baltimore Orioles pitcher Mike Cuellar. Ashby finished the 1973 season appearing in 11 games with Cleveland, batting .172 with 1 HR and 2 RBI.