Born in Saint Petersburg in 1947, Bezverkhny commenced his violin studies at the age of 5 at the Central Music School of the Conservatory of Saint Petersburg. He was a student of Liubov Segal (student of Leopold Auer) and Jacob Riabinkov. In 1965 he started his studies at the Moscow Conservatory under Yuri Yankelevich - one of the most prominent violin professors of the 20th century. He also studied with Maya Gleyzarova, Abram Stern and Nahum Latinsky. He is laureate of several international competitions:
1967: 2nd prize Wieniawski Competition
1969: 2nd prize chamber music competition in Munich
1972: 2nd prize violin competition in Montreal
1972: 1st prize chamber music competition in Belgrade
1974: 1st prize chamber music competition in Budapest
1976: 1st prize Queen Elisabeth Competition Brussels
In 1978 he was barred from leaving the USSR. In February 1990 he settled in Belgium. Since October 1992, Bezverkhny has been a member of the Shostakovich Trio, and his recordings for Melodya and Deutsche Grammophon now number more than forty. During all these years he has been very intensely active as a violinist, a violist, a composer, a director and an actor. Currently he is teacher at the Royal Conservatory of Gent.  His students include amongst others Dmitri Berlinsky.
As a composer, he wrote a virtuoso Suite Gambrinus for violin and piano.