A strong right-handed pitcher, Bob was the first players selected in the 1972 Major League Baseball draft and the No. 1 draft choice of the Los Angeles Dodgers. The previous year, he had been drafted by the Pittsburgh Pirates, but did not sign a contract.

Leslie played six seasons in the minor leagues for the Dodgers and California Angels, wrapping up high minor league career with the Triple A Salt Lake City Gulls in the Pacific Coast League. Bob attended spring training with the Dodgers in 1974, 1975 and 1976.