Bush began his career in the youth academy of Brentford before moving to the youth setup at Metropolitan Police. He then joined the first team at Metropolitan Police and made over 100 appearances for the club. In 2012, he signed for Conference South club Dover Athletic, where he spent two seasons before moving to Football League side Hereford United. Bush then went on to play for Gateshead and Lincoln City before joining Boreham Wood in 2018.