Following a goalless draw at Gigg Lane in the original tie a week last Saturday, Parkinson's men and the Shakers will meet for a third time so far this season on Tuesday for the right to host Championship side Hull City in the fourth round.
The Bantams secured a 2-1 victory at the Coral Windows Stadium in the first league meeting of the campaign between the two clubs back in October - a result which kicked off City's current eight-match unbeaten run on home soil.
Parkinson said: "We've had two tight games against them so far and I expect this one to be no different.
"We've obviously won the first one, the second one we have probably shaded it going on chances created.
"Both were hard-fought games and there will be no quarter given on Tuesday night either.
"There is a big prize at stake for the winners - a home tie in the FA Cup fourth round against a side flying high in the Championship.
"We have worked hard to get to this stage of this year's competition and we want to finish the job off and try to get ourselves that tie with Hull City in the fourth round. It is going to need one almighty effort to do that though."
Steven Davies continues to train with the rest of the squad as he builds up his fitness following the serious knee injury he picked up, ironically, during Bury's previous visit to Valley Parade in October.
Parkinson says Davies isn't expected to start a game anytime soon but with the Bury replay the second of five games in two weeks for City, the Bantams chief has suggested that he could look to freshen things up soon.
He added: "Steven has been progressing well in training and there has been no reaction from his knee.
"We must stress that he is still some way off starting a match at the moment but he has an outside chance of making the bench for maybe one of our games coming up.
"He's had a few days of training now and he is going closer to being back involved.
"We have a lot of games coming up and we will make changes when we feel it is the right time to do so.
"Hans (James Hanson) got a slight knock on his calf and Billy Clarke got a minor dead leg on Saturday (vs Oldham Athletic) so we will assess those two over the next 24 hours.
"We will be picking a team which we feel is ready and able to put in a really committed performance."
Speaking ahead of Tuesday's replay, Parkinson also confirmed press reports that Sky Bet League 2 side Carlisle United have made an approach for Gary Liddle.