David Amoo put Bury ahead from a quick counter-attack in the 10th minute, racing clear on to Steven Schumacher’s defence-splitting pass to coolly round David Martin and slot home.
But Bowditch equalised for the Dons 10 minutes later when he stooped to nod in from close range after Daniel Powell’s cross had been flicked on by Charlie MacDonald.
MacDonald then fired against a post from an acute angle before Shakers midfielder Giles Coke – who had been booked early on for a rash tackle – was shown a second yellow card for hauling back Powell.
Bowditch made the Dons’ numerical advantage count just a minute later, sending Cameron Belford the wrong way from the penalty spot after the ‘keeper had tripped MacDonald in the box.
The Dons controlled the second half but Mark Hughes almost snatched an unlikely point for the Shakers at the death when he volleyed tamely at Martin from close range.