Bostock began at the age of seven playing football at Crystal Palace. On 29 October 2007, he made his debut for Crystal Palace against Watford. When he was 15 years and 287 days old. Tottenham Hotspur on 30 May 2008, the arrival of the then 16-year-old Bostock known. During his time at Tottenham, he was loaned to Brentford, Hull City, Sheffield Wednesday, Swindon Town and the Canadian Toronto FC. On 7 June 2013 confirmed the Premier League that Bostock end contract was at Tottenham. On 11 July 2013, he signed a two-year contract with Royal Antwerp FC.
Bostock played for various English national youth teams. He earned 25 caps for England under-17 and 9 more caps for England-19