Bujones has directed Orlando Ballet since 2000. He is a former principal dancer with American Ballet Theatre, and in 1974 became the first American to win the International Ballet Competition's gold medal. In over 30 years of performing, he appeared with, among other companies, the Royal Ballet, the Paris Opera, and the Stuttgart Ballet. His choreographic works have been performed by ABT, the National Ballet of Canada, Boston Ballet, Atlanta Ballet, and Tokyo Ballet.
In 1994 he founded the Madrid-based company Ballet Clasico Mediterraneo.