Born November 1, 1931 in Tbilisi, Georgia. Took piano training at the ten-year music school at Saint Petersburg Conservatory named after A.D. Virsaladze.
In 1950-1955, studied at the Moscow Conservatory in the class of A.B. Goldenveizer, and continued the training at the graduate school under his supervision until 1957.
In 1955, became the winner of M. Long- J. Thibaud International Competition in Paris.
From 1957 to 1991, taught special piano classes at the Moscow Conservatory (at first, as an assistant to professor A.B. Goldenveiser), while since 1977 as a professor. Also taught at the Kiev Conservatory.
Since 1987, a professor and one of the founders of the Queen Sophia Higher School in Madrid.
Since 1992, Bashkirov has been a full professor of the Como Musical Academy (Italy).
Awarded by the Order of King Alfonso X for the merits in the field of culture and education (Spain), Honorary Medal of the Madrid University, Robert Schumann Honorary Medal, Honorary Sign of the Russian Piano Players Festival (Germany) and Honoris Causa Professorship of the Shanghai Conservatory (China).
Over half a century of concert activity has been performing with constant success in hundreds of cities of the USSR and other countries. The partners of his concerts with symphony orchestras were such conductors as E.Svetlanov, K.Kondrashin, D. Oistrakh, J. Sall, G. Rozhdestvensky, Yu. Temirkanov, R. Barshay, J. Barbirolli, P. Pare, K. Sanderling, K. Zekki, I. Markevich, K. Mazur, D. Barenboim, T. Berglund, etc.
Bashkirov was a soloist in the concerts by outstanding collectives: Leningrad and Moscow Philharmonic Orchestras, the State Symphony Orchestra and Grand Symphony Orchestra, the Vienna Philharmonic Orchestra, Royal Philharmonic Orchestra (London), Chicago and Cleveland Orchestras, Gewandhaus Orchestra and Orchestra de Paris, the Israel Philharmonic, Helsinki, Bucharest and Belgrad philharmonic orchestras, and the orchestras of the largest cities of the former USSR.
Bashkirov runs master-classes on a continuous basis: at the Paris National Conservatory, Mozarteum Summer School in Zalzburg, J. Sibelius Academy in Helsinki and at the Como lake in Italy. Besides, he regularly takes part in the award panels of multiple international competitions.
In 2007, he was an award panel member of the 13th International Tchaikovsky Competition.
His repertoire includes the works by W.A. Mozart (one of his best interpreters), L. van Beethoven, F. Schubert, R, Schumann, J. Brahms, C. Debussy, S.S. Prokofiev, G.G. Galynin, and others.