Buddy grew up in Harrisburg, PA and was primarily a self taught dancer, picking up the dances of the day, he became very good. Buddy's Father died when he was just a child and was raised by his religious mother, but by the age of fourteen his mother had passed away which led Buddy to Utica, New York where he stayed at Mrs. Douglas 133rd St. Boarding House temporarily working as a hotel busboy. This Boarding House is where Buddy would get his calling to entertain as the House was full of entertainers and show people. Bradley would practice his steps in a back alley near Connie's Inn, unknowingly honing his craft.

Buddy's first professional job as a dancer was at the Kentucky Club and Connie's Inn (Uptown) when his friend Thaddeus Drayton recommended him to Leonard Harper who was producing the shows at these clubs. Harper needed Chorus Boys and hired him on the spot, where he remained at Connie's Inn, learning his skills for over a year, becoming one of the best young dancers of Harlem.

Continuing to dance when he turned eighteen he made his solo debut as a dancer in the Florence Mills Revue in New York. In 1928, Buddy met Billy Pierce, who wanted to start a dance studio for white stars, such as Fred Astaire, Lucille Ball, Mae West, and Eleanor Powell and more. Buddy was hired to teach them the popular dances of the day. Bradley met and was hired to coach Irene Delroy in a dance routine for the Greenwich Follies of 1928 at the Imperial Theatre. This would prove to be his big break as Irene was a hit with the show and the producer of the show Morris Green asked Bradley to re choreograph the entire production, however Busby Berkley would get the credit.

Bradley gives credit to dancer and Stage performer Eddie Rector, and claims Rector as Buddy's mentor and idol. Buddy was not the best solo dancer but his choreography during this time period was amazing. He had a great talent for translating the accents of improvising jazz soloists into dance patterns that were new to Broadway as well as an eye for designing dance steps to fit the individual dancers personality. Bradley generally ignored the melody and followed the soloists to get a fresh rhythmic pattern to his steps. He was so good in fact that he would go on to either fix or stage many dances for many Broadway Stage revues such as "Ziegfeld Follies", George White "Scandals", "Earl Carroll's Revues" and Lew Leslie’s "Blackbirds" during the nineteen-twenties and thirties, however because of his color he never got credit while in the USA.

In 1933 Buddy was hired by Charles Cochran (The Ziegfeld of England) and went to London to Stage the shows on the Rodgers and Hart musical "Evergreen". It was the first time a black dancer had choreographed and Staged an all white show. Bradley made many trips back and forth from England to the States, but eventually made his home in England were he taught, Staged and Choreographed for many Stage, Film and TV Shows well into the 1960s. When Buddy left the states, Pierce replaced Buddy with Herbie Holder. Frank Harrington and Roland Holder were assistants to Bradley.

Buddy would join forces on many projects with many well known dance stars such as George Balanchine, Anton Dolin and Vera Zorina, Massine, Frederick Ashton and Markova for Sadler Wells. Basically Buddy was the best kept secret in dance choreography. Buddy passed away in 1972 in New York, New York.