Born in Žáky in Bohemia, his musical talents were first noticed at age of eight, and at age fifteen he traveled to Prague to study piano and composition with Václav Tomášek. By the age of twenty, Dreyshock undertook his first professional tour in December 1838, performing in various northern and central towns in Germany.
Subsequent tours saw Alexander visiting Russia (1840–42); Paris (spring 1843); London, the Netherlands, Austria and Hungary (1846); and Denmark and Sweden in 1849. Elsewhere he caused a sensation with prodigious execution of thirds, sixths, and octaves, plus other tricks. When he made his Paris debut in 1843 he included a piece for the left hand alone. Dreyschock’s left-hand was renowned, and his most famous technical stunt was to play the left-hand arpeggios of Chopin’s Revolutionary Étude in octaves. Observers of the time report that he played it in correct tempo, and it is known that he programmed it in all of his recitals.