He won many competitions, including first prize at the Valentino Bucchi Competition, First Prize at the Torneo Internazionale della Musica and a second prize in the string competition Nicanor Zabaleta.
Principal Double Bass player for 5 years in the “Orchestra Nazionale dell’Accademia di Santa Cecilia” (Rome) and for 15 years in the Orchestra “”del Maggio Musicale Fiorentino (dir. Zubin Metha). He appeares in the same role with numerous orchestras including the Orchestra of the Teatro alla Scala (Milan), London Symphony Orchestra (London), the Solisti Veneti, Tokyo Symphony Orchestra (Japan), Orchestra del Teatro Massimo di Palermo, Berliner Symphoniker, I Solisti Filarmonici Italiani, Orchestra di Roma e del Lazio.
As a chamber musician, Alberto Bocini played with Yuri Bashmet, Vadim Repin, Patrick Gallois, Natalia Gutman and Eric Ruske. The Newport Music Festival has honored him by inviting eleven times until 2004.
Alberto Bocini is a member of Bass Gang, a quartet of bass in extremely heterogeneous repertoire in its musical choices, presented with virtuosity and irony. The quartet has a great success and was acclaimed in Japan and Korea. They recorded a DVD for the independent label NBB Records, founded by Alberto Bocini brand, for which he has recorded.
Eclectic and enthusiastic musician, Alberto Bocini does not hesitate to push the boundaries of his repertoire. It has engraved for Denon Braevissimo, concerto for double bass and strings of Ennio Morricone, or a dedicated disk to the music of British rock band Genesis with a trio named “After Genesis”.
As a soloist he has recorded for Denon, Stradivarius, Velut Luna, NBBrecords.
Since 2009 Alberto Bocini is professor at the HEM /Haute Ecole de Musique de Genève.