Skipper Keith Andrews' early goal had given MK the lead but Bishop struck either side of Dons defender Drissa Diallo's straight red card to ensure Ince's reign got off to the worst possible start.
The Dons dominated early on with some neat passing football and Andrews deservedly put them ahead in the 21st minute. He raced onto Kevin Gallen's knock-down and belted a swerving 22-yard half-volley past flat-footed Bury keeper Jim Provett and into the corner of the net.
Jon-Paul McGovern almost doubled the Dons' lead six minutes later but his well-flighted 23-yard free-kick curled just past the post and into the side netting.
Bury battled back and Paul Scott looped a 10-yard header just over the bar before Glynn Hurst missed two good chances, first blasting wide off-balance from close-range and then firing tamely at Dons' new keeper Willy Gueret when well placed 16 yards out.
Yet the Dons continued to press and Andrews' 35-yard thunderbolt was saved low by the diving Provett before Leon Knight poorly curled straight at the Shakers' keeper when one-on-one from Gallen's clever 36th minute through ball.
But Bury burst out of the blocks after the break and substitute Bishop equalised in the 51st minute, just minutes after he had been denied one-on-one by Gueret.
Dons skipper Andrews looked to have cut out Nicky Adams' low cross at the near post but Bishop robbed him of possession and tucked the ball low past Gueret from close-range.
And then Bishop's cool 58th minute penalty turned the game on its head and put the Shakers 2-1 up. Bishop sent Gueret the wrong way from the spot after Dons defender Diallo had been shown a straight red card for elbowing Ben Futcher.
MK's 10-men toiled hard late on in search of an equaliser but they rarely threatened as Bury stood firm to record a battling comeback win.