Richard Wilkins' side went into the interval one down to a 13th minute Prince M`Bengui effort, despite playing some neat football and twice striking the crossbar.
But eight minutes into the second half Bullard smashed home his first following a goal mouth scramble. Three minutes later and the Blues had Seb Dunbar dismissed for what appeared to be a harsh red card.
Then, two goals in less than 60 seconds midway through the second half turned the game on its head. First skipper Bullard fired home with a cultured left foot volley and then Gareth Heath angled a drive low into the bottom left hand corner to seal the win.
Ryman League
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