Having had a trial period with the club in February 1998, Bulman joined Wycombe Wanderers in the summer of 1998 for a fee of £10,000. Bulman made his debut as a late substitute in a 1–1 draw at home to Bristol Rovers on 31 August 1998, and within 15 seconds of coming on the pitch, he scored as Lee Jones' clearance had deflected off his buttocks and into the net. Bulman went on to make a further 10 appearances for the club across the 1998–99 season. Bulman spent six years at the club and played in an FA Cup semi-final against Liverpool in 2001.
Stevenage and Crawley Town
He transferred to non-league Stevenage Borough in 2004 after his contract at Wycombe Wanderers expired. He joined Crawley on a three-month loanin September 2006, with a recall clause after 30 days. His debut for the club came as a substitute on 2 September 2006 in a 2–0 defeat at home to Northwich Victoria. After making 15 league appearances on loan at Crawley, scoring thrice, he left Stevenage after his contract was cancelled by mutual consent in early December 2007. Bulman joined Crawley Town on a permanent basis in January 2007.
He signed for Oxford United in May 2009 on a two-year contract. He made his competitive debut for the club on 8 August 2009 in a 2–1 home victory against York City on 8 August 2009, before going on to win promotion from the Football Conference with Oxford. He returned to Crawley Town on a three-month-long loan in September 2010. In January 2011, he agreed to sign permanently for Crawley on a free transfer. He won promotion to the Football League with Crawley after they won the Conference in the 2010–11 season, whilst they also reached the fifth round of the FA Cup, before being knocked out by Manchester United. The 2011–12 season saw Crawley promoted again, this time to League One as they finished 3rd in League Two.
In June 2014, Bulman signed for AFC Wimbledon on a free transfer. He made his debut for the club in their first match of the season, starting in a 2–2 draw at home to Shrewsbury Town on 9 August 2014.
Second return to Crawley Town
He returned to Crawley in 2017, and was offered a new contract at the end of the 2017–18 season. In June 2019, at the age of 40, Bulman was offered another one-year contract by Crawley; at that point he was the oldest active player in the English Football League, ahead of Kevin Ellison, Aaron Wilbraham and James Coppinger. At the end of the 2019–20 season, he was offered a new contract by the club.
