Myron Carlton "Tiny" Bradshaw was born on September 23, 1907, in Youngstown, Ohio. He graduated from Wilberforce University with a degree in psychology before pursuing a career in music. Initially, he played drums and sang with Horace Henderson's Collegians in Ohio. In 1932, Bradshaw moved to New York City, where he performed with various bands, including Marion Hardy's Alabamians and the Mills Blue Rhythm Band.

In 1934, Bradshaw formed his own swing orchestra, which recorded for Decca Records. Over the years, his music evolved towards rhythm and blues, and he recorded extensively for King Records from 1949 to 1955, producing several hits on the Billboard R&B chart. His song "Well Oh Well" reached number two on the R&B chart in 1950. Although "The Train Kept A-Rollin'" was not a chart hit, it became a pivotal song in the development of rock and roll, later covered by artists like The Yardbirds and Aerosmith.

Bradshaw's band was known for its lively performances and featured notable musicians like Red Prysock. Despite suffering two strokes, Bradshaw continued to perform until his health declined. He passed away on November 26, 1958, in Cincinnati, Ohio, leaving a legacy as a pioneering figure in the transition from jazz and swing to rhythm and blues and rock and roll.