Born in Miami of Cuban parents, Bujones was one of the finest male dancers of the 20th century, hailed as one of the greatest American male dancers. In 1967, he won a scholarship to the School of American Ballet of the NYC Ballet Company.
In 1974, he won the Gold Medal at the International Ballet Competition in Bulgaria.
He would then become a soloist for the American Ballet Theater and then Principal Dancer working with Mikhail Baryshnikov.