Bumgarner, who is expected to pitch for San Francisco in next week's NL wild-card game, accepted the award in a 15-minute ceremony prior to Friday night's home game against the San Diego Padres.
Several past winners of the award were on hand, including Dave Dravecky, Bob Brenly, Darrell Evans, J.T. Snow and Jeff Kent.
McCovey, however, did not attend. The 76-year-old remains hospitalized following complications from an infection.
The ''Willie Mac'' Award is voted on by the players, coaches and training staff to recognize the team's most inspirational player both on the field and in the clubhouse. Bumgarner is 18-10 with a 2.98 ERA.