The article discusses the features of personalization of the competence training for bachelors of art and pedagogical direction. Four characteristics of the essence of the personalization for the educational process are presented. Personalization of bachelor's degree training in the art and pedagogical direction is an unique way for a person to master and appropriate the richest potential of artistic culture. The potential of distance technologies has been identified, which contributes to the personalization of the competence training of bachelors of art and pedagogical direction. Firstly, distance technologies activate the subject position of the student. In the behavioral aspect, a bachelor of art and pedagogical direction, entering the position of the subject, must build his own educational trajectory, and in the sense-forming aspect, he must build his own relationship with the world of art. Secondly, they enhance the openness of the educational process. Thirdly, they actualize such personality qualities as initiative and creativity.