Bidelman was elected to the American Astronomical Society in 1944. and was a member for over 65 years. He was president of the Cleveland Astronomical Society from 1973 to 1976. Bidelman was elected to the international science honor society Sigma Xi by Case Western Reserve University. The minor planet 9398 Bidelman (1994 SH3), discovered by the Arizona group Spacewatch at Kitt Peak on September 28, 1994, was named in his honor. It is an outer main belt asteroid. The peculiar supergiant star HD 30353 is named "Bidelman's star".