Born in Córdoba, Bessone spent four years as a youth player at Spanish club Barcelona, alongside Lionel Messi, who he had grown up with.

[5][6] On 21 January 2011, Bessone moved to Charlton Athletic on a loan deal until the end of the season, with the option of a permanent transfer.

[7] In February 2011, Bessone gave an interview to the Yorkshire Evening Post where he admitted his performances for Leeds has been "opened to close scrutiny.

[10] After failing to find a new club, Bessone returned to training with Leeds United in June 2011,[11] and he was later named in their squad for a friendly tour of Scotland.

[12] On 31 August 2011, Bessone had his contract with Leeds cancelled by mutual consent, and he re-joined Swansea that same day,[13] to provide defensive cover for the injured Alan Tate.