Bascomb was a founding member of the Bama State Collegians, which was led by Erskine Hawkins and eventually became his big band. Bascomb's brother Dud played in this ensemble as well. Bascomb remained in this ensemble until 1944, aside from a brief interval in 1938–39 where he played in Count Basie's orchestra after Herschel Evans's death. From 1944 to 1947 he and Dud co-led a septet which evolved into a big band. He recorded for States Records in 1952; these sides were reissued by Delmark Records in the 1970s. From 1953 to 1955 he recorded for Parrot. He was active as a performer nearly up until the time of his death.