Bozkurt began his coaching career whilst playing for Hampton & Richmond Borough. He was appointed as the academy goalkeeping coach at Leyton Orient on 1 February 2016. Bozkurt held this position until 1 April 2017, when he became the club's senior goalkeeping coach.[3]
On 7 August 2017, he moved as a player-coach to Boreham Wood.[4] Bozkurt retired as a player on 18 January 2018, when he left his position as goalkeeping coach at Boreham Wood for the equivalent U21 position at EFL Championship side Queens Park Rangers.[5] He would be promoted to the role of first team goalkeeping coach on 4 June 2020,[5] ahead of the restart of football following the COVID-19 pandemic. On 4 February 2023, Bozkurt would leave QPR for Wycombe Wanderers[6] in what would be a brief spell that lasted under a month.[7] On 30 June 2023, he became the goalkeeping coach of MK Dons under manager Graham Alexander.[8]
On 5 July 2024, Hull City appointed Bozkurt as their first team goalkeeping coach.[1] As a result of a touchline fight with Peter Murphy during Hull's 3–0 win over Preston North End on 20 January 2026, Bozkurt was sent off and later received a one-match ban and £1,000 fine. Murphy, who was also sent off, was punished with a one-match ban and a £2,000 fine.[9][10]