when did he conduct bach?
1829
Felix Mendelssohn
In 1829, with the backing of Zelter and the assistance of the actor Eduard Devrient, Mendelssohn arranged and conducted a performance in Berlin of Bach's "St Matthew Passion". 
who was widely known as the most outstanding violin virtuoso of the 19th century Jakob Ludwig Felix Mendelssohn Bartholdy
wiki:13451667
Felix Mendelssohn [SEP] Meeting Goethe and conducting Bach
Four years previously his grandmother, Bella Salomon, had given him a copy of the manuscript of this (by then all-but-forgotten) masterpiece. The orchestra and choir for the performance were provided by the Berlin Singakademie. The success of this performance, one of the very few since Bach's death and the first ever outside of Leipzig, was the central event in the revival of Bach's music in Germany and, eventually, throughout Europe. It earned Mendelssohn widespread acclaim at the age of 20. It also led to one of the few explicit references which Mendelssohn made to his origins: "To think that it took an actor and a Jew's son to revive the greatest Christian music for the world!"