It was looking as though the Alex were heading for victory when substitute Brad Inman fired them in front clinically with just eight minutes left, but in the final of four minutes of added time Bury skipper Steven Schumacher was felled by Mark Ellis and Bishop beat Steve Phillips from 12 yards to earn a much-needed point.
Asked initially about the late penalty, Davis said: "I haven't seen it clearly yet, but I think the ball probably should have been cleared before the lad races into the box. The ball's gone up in the air, their lad has fallen over and a penalty has been given.
"It's disappointing, but it's been a tough day all round.
"We knew we'd have the long ball to contend with and a really physical approach, and to be honest we did well to cope with that and go in front towards the end as we did.
"It had been a bit frustrating up to that point. We hadn't created too much apart from the goal in the first half, but the three substitutions in the second half really did make a big difference.
"They gave us that extra impetus and once we'd gone 2-1 up we really ought to have seen the game through.
"We missed a great chance to go 3-1 up towards the end and that would have finished the game off, but Bury are a tough outfit, especially here, and they're fighting for everything."