Bassedas is a product of Vélez Sársfield youth divisions, club where he debuted professionally on 3 March 1991. He played as a sweeper (libero), and was an important part of Vélez most successful years during the 1990s. He won four national championships with the club, and five international (including the 1994 Intercontinental Cup, where he was a starter in the 2–0 victory over A.C. Milan).