Born in Johnson City, Tennessee, he batted and threw right-handed, stood 5 feet 10 inches (1.78 m) tall and weighed 160 pounds (73 kg).

As a member of the San Francisco Giants, he served as the primary backup to the club's regular shortstop, José Pagán, and second baseman, Chuck Hiller.

On August 23, his only MLB home run off Al Jackson of the New York Mets at the Polo Grounds was a key blow in San Francisco's 2–1 victory.

In the latter series, Bowman batted once against Marshall Bridges in Game 4 at Yankee Stadium and flied out to right fielder Roger Maris.

At the end of the season, he was traded to the Milwaukee Braves in a seven-player deal whose principals included Felipe Alou, Ed Bailey, Bob Shaw and Del Crandall.