Wilber signed with the American League St. Louis Browns in 1938, but was acquired by the Cardinals in 1940 and played in their extensive farm system until the outbreak of World War II; he missed the 1942–45 seasons while serving in the United States Army Air Force, where he attained the rank of captain.

In 1946, he resumed his baseball career and made his Major League debut, appearing in four games before being sent to the Triple-A Columbus Red Birds.

On August 27, 1951, Wilber hit three home runs off pitcher Ken Raffensberger, each on the first pitch of each at bat, to lead the Phillies to a 3–0 victory over the Cincinnati Reds.

Then, after hanging up his catching gear, he managed at the Triple-A level with the Louisville Colonels, Houston Buffs of the American Association, Charleston Senators, Tacoma Twins, Denver Bears and Spokane Indians.

His one-game stint as skipper of the 1973 Texas Rangers—as interim pilot between Whitey Herzog and Billy Martin on September 7, he won his only game as manager,[5] 10–8 against the future world champion Oakland Athletics—occurred after Wilber led the Rangers' Spokane affiliate to the 1973 championship of the Pacific Coast League, one of three league titles in his minor-league resume.

After his baseball career, Bob Wilber worked in international sports marketing, was chief executive (GM) of three different professional indoor soccer franchises (St. Louis Storm, Kansas City Attack, and Indianapolis Twisters).