The Black Cats' evening started in the worst possible fashion when midfielder Arnau Riera was sent off with less than three minutes gone.
Making his first start for the club, Riera caught Richie Baker with his arm and was shown a red card by referee Michael Jones.
Sunderland held on until eight minutes from time, Bury defender Fitzgerald rising to meet Brian Barry-Murphy's corner at the near post and smashing a header past Ben Alnwick.
Fitzgerald, who had already been booked, jumped straight into the crowd and was sent off for his second yellow card.
Four minutes later Bishop sprung the offside trap to clip the ball past Alnwick and seal victory.
Following Kevin Phillips' decision to move to West Brom rather than his old club, things went from bad to worse for Sunderland chairman and manager Niall Quinn as his side lost their fifth consecutive match.
Having seen the Shakers' Nicky Adams fluff a golden chance after he had latched onto a poor Kenny Cunningham backpass, the visitors had looked in control in the second half, with Stephen Elliott threatening on a couple of occasions.