The game also saw the welcome return to action of Tom Smith and Greg Cunningham, who both suffered broken legs in the second half of last season.
Irish international Cunningham was back in sky blue after a loan spell at Leicester, and he kept City in the lead with a vital goal-line clearance midway through the second half.
City had taken the lead in the 12th minute when Bunn pounced on a defensive lapse, but the striker spurned the chance to double the lead when he struck the post from the penalty spot four minutes later.
Smith also hit the woodwork before the break, and goalkeeper Tom Halsall ensured City stayed ahead late on with a fine save from a free kick.
Team: Halsall, Smith, Cunningham, Chantler, Veseli, Meppen-Walter, Roman (Clowes), A Mancini (Robinson), Bunn, Assulin, F Mancini (Helan).
