Mosby toured with the Tennessee Ten in the 1910s, and also led his own ensemble in Chicago. He then moved to California early in the 1920s, where he opened a record store and then toured with Mamie Smith. He also led a band called the Blue Blowers in California. He took an extended residency in 1924 at Solomon's Dance Pavilion in Los Angeles; this ensemble recorded privately, and some of these cuts have survived. The band recorded for Columbia Records in 1927, and included Jake Porter, Les Hite, and Henry Starr as sidemen. In 1927 they played at the Bronx Palm Gardens and in 1928 at the Lincoln Theater.
Mosby opened his own nightclub, the Apex, in 1928, and his band appeared in the films Thunderbolt and King Vidor's Hallelujah the next year. Late in 1929 a police raid shut the club down, but he reopened after an acquittal soon after. He opened another club in San Francisco at the end of 1930. He went bankrupt in 1931, and moved to San Francisco. Over the course of the 1930s he opened several clubs, not all of them successful, along the California coastline; musicians who appeared in his bands included Lawrence Brown, Marshal Royal, Wilbert Baranco, Baron Moorehead, and Buck Clayton. His successful Club Alabam featured Harlan Leonard in 1943, Roy Milton in 1944, and Johnny Otis in 1945, all in succession. He was jailed for tax evasion from 1947 to 1949 and lost control of his clubs; after serving his time, he reopened some of them and then permanently moved to San Francisco.