Bickford was born in Kentucky but raised in West Virginia. He began his professional career in 1939 and, after serving in World War II, made the majors in 1949. Acquired by the Braves organization due to a flip of a coin, Bickford became one of the most promising National League pitchers during his playing career, earning All-Star honors in 1949 and leading the National League in complete games in 1950. However his career was soon shorted by multiple arm injuries, and he was out of baseball by 1955. After working an assortment of jobs, he was diagnosed with stomach cancer in 1960 and died after a three-month illness.