In 2005 Kuzma graduated from the P. I. Tchaikovsky Moscow State Conservatory and completed his graduate studies in composition under the direction of professor A. V. Tchaikovsky in 2008.

An award-winning composer, Kuzma has created original music for theater, opera, motion pictures, animated films, chamber instrumental compositions, arrangements for ensembles, orchestra and choir. He is the author of several works written for the mass of His Holiness Pope Benedict XVI (JMJ Madrid, 2011).

Kuzma collaborates with «Universal Edition» Publishing House in Vienna and in 2011 had been named "Person of the Year" by the Muzykalnoe Obozrenie (Music Review) Newspaper. In 2008, he received a prize from composers radio «Deutsche Welle» (Bonn, Germany) and in 2013, acted as musical director of "Tales of the Old Piano", an educational animated film project, which garnered an award from the Government of the Russian Federation.​

He is composer-in-residence with JMJ Orchestra in Madrid, visiting professor at the Katarina Gursky Higher School of Music in Madrid and teaches at the P. I. Tchaikovsky Moscow Conservatory.

He recently collaborated with director Pavel Lungin on the feature Queen Of Spades, based on Pushkin's classic, adapted for the screen by David Seidler (The King's Speech).  

Kuzma Bodrov's music is performed by the Tchaikovsky Symphony Orchestra of Moscow, Evgeny Svetlanov State Academic Symphony Orchestra, Academic Symphony Orchestra of the Moscow Philharmonic, Glinka Capella Symphony Orchestra, State Hermitage Orchestra «St.Petersburg Camerata», amongst others.

Major compositions include Opera H.M. Mixed Media, Capriccio for Violin and Orchestra, Sinfonietta For Chamber Orchestra, Symphony for Full Symphony Orchestra & others.