Slough-born Bressington enjoyed a promising start to his career, being a member, alongside Kevin Keen and Mark West, of the High Wycombe Schools U15 side which won the ESFA Trophy in 1981 and enjoying spells with Chelsea and Arsenal as a junior.
Having impressed in a GM Vauxhall Conference match against Lincoln City, Bressington was signed by the Imps for £20,000 in November 1987 and went on to play his part in the club's GMVC Championship success, making 13 appearances in the competition.
Bressington linked up with Southend United, managed by the man who signed him for Lincoln City, Colin Murphy, for £25,000 in the summer of 1993 but once again, injuries curtailed his Football League outings during his time at Roots Hall and caused his retirement from the professional game in the summer of 1995.
He made a handful of appearances for hometown club Slough Town at the beginning of the 1995–96 season but injuries again took their toll and he began to wind down his senior career.
He was even drafted into their first team for a game in March 2006 when, four months before his 40th birthday, he turned out in their match against Dunstable.