Bassedas is a product of Vélez Sársfield youth divisions, club where he debuted professionally on 3 March 1991. He played as an 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).
In 2000 he joined English FA Premier League club Newcastle United for £3,500,000. He played for them in the period 2000–2003, though on loan to Tenerife briefly during the 2001–02 season. He scored once in the league for Newcastle in a 3-1 defeat at Chelsea in January 2001.
In 2003 he joined Argentine Newell's Old Boys, but after two months of pre-season training he decided to retire from football at the age of 30.