Bullivant was a midfielder during his playing days, signed as an apprentice in May 1974 to Fulham FC and transferred to Aston Villa FC for £220,000 in November 1979.
Playing 108 times and making another 7 as subtitute scoring 2 goals for Fulham.
He later managed Barnet, and later Reading before resigning following a run of poor results.
He then coached at Brentford, followed by a spell at Crystal Palace, where he briefly took the reins as caretaker manager alongside Steve Kember after Steve Bruce's resignation.
In October 2004 Bullivant left Crystal Palace to become first-team coach at Watford, who had lost previous incumbent Terry Burton to Cardiff City. When manager Ray Lewington was relieved of his duties in March 2005, Bullivant became joint caretaker manager alongside Nigel Gibbs. Watford appointed Adrian Boothroyd as Lewington's replacement, and he created a new management team. Bullivant departed without presiding over a single game.
He subsequently joined the coaching staff at Birmingham City, until a clearout of backroom staff following relegation from the Premier League, saw Bullivant released by the Blues in June 2006.
He returned to Brentford on 11 March 2008 as Andy Scott's Assistant Manager.