With an hour gone the Shots were dead and buried, but a stirring ten-minute come back salvaged a point for the Hampshire club.
On the 20-minute mark, Mikhael Jaimez-Ruiz on his league debut almost gifted Bury a goal.
When he failed to clear, Andy Morrell chipped the ball goalbound only to see it bounce out off the underside of the crossbar.
Louis Soares then desperately scrambled the ball to safety with Andy Bishop ready to pounce.
Bury took the lead on 25 minutes with a well-crafted goal. Michael Jones' 40-yard pass found Elliot Bennett and the striker cut the ball back to Bishop, who found the bottom left corner of the net.
Bury doubled their lead when Paul Scott was left unmarked at the back post to head home the simplest of chances from Brian Barry-Murphy's corner kick.
On 59 minutes, Bishop appeared to finish the contest with a powerful free-kick from the edge of the penalty box.
Ten minutes later, Aldershot pulled a goal back through substitute Rob Elvins. Hudson was again the provider as Elvins headed home from six yards.
Bury inexplicably fell asleep and Scott gave away a needless penalty with 15 minutes left.
Under no real pressure, the Bury captain hand balled Hudson's cross and Scott Davies smashed home convincingly after some gamesmanship from Brown.
Aldershot were now in the ascendancy and completed a stirring comeback when Danny Hylton silenced his boo-boys with 10 minutes to go.
When the former Aldershot academy player picked the ball up 40 yards from goal there appeared little danger.
However, Hylton had other ideas after jinking his way past three defenders and driving the into the bottom left corner from 16 yards.