A set-piece opener from Rory McArdle on the stroke of half-time, plus an own goal from former Bantams loanee Reece Brown from another corner six minutes after the break, helped secure City their third league win on the trot for the first time in over two years.
Bury substitute Danny Rose caused some late drama in the final seconds when he pulled one back with a fine volley deep into stoppage time but a determined City weren't to be denied.
For the visitors, it was only their second league defeat of the season, their first defeat in the Sky Bet League 1 in twelve games, and the first time they had failed to pick anything up from a league away game since 31 January this year.
Parkinson said: "As I mentioned after the Doncaster game on Saturday, we had a meeting with the boys on Monday and it was the lads who mentioned everything that we needed to show at home, and they went out and put that into practice tonight (Tuesday).
"You can see why Bury have won a lot of games away from home - they are a good side - but we were resolute and we stuck to our task. The set-play goals were pleasing as well.
"We have been practicing them a lot recently and showing the lads footage of our set-pieces and giving them details on how we can improve.
"Having that desire to go in there and stick your head in for the ball in that final yard is crucial as well though, and Rory McArdle showed that with his goal.
"The players were terrific the whole night and it was just a shame that we conceded right at the end because the back four and Ben (Williams) deserved a clean sheet for their performance.
"Bury invested wisely in two good strikers over the summer in Leon Clarke and Tom Pope but I thought the back four handled them well. They seemed to take their performance at Doncaster into tonight.
"I've sensed a growing determination about the lads in recent weeks and they were really keen to show that spirit and resiliency in front of the home fans.
"We won't be patting ourselves on the back too much after this win though. The preparation for Wigan (Athletic) on Saturday begins now."
The only low point of the whole night came when Steven Davies limped off with a knee problem shortly after City's second goal early after the interval.
Parkinson added: "He's unfortunately hurt his medial knee ligament, which is obviously a big blow for him and for us.
"His toughness out on the pitch has been a real bonus for us in recent weeks and we just hope it isn't too serious for him.
"On the flip side though, I was pleased with how James Hanson played when he came on.
"He is an important player for us and we need him firing on all cylinders.
"We are doing everything we can as a group of staff to help him to be the threat that we know he can be.
"Tonight he certainly showed signs he was getting back to that."
Although Davies looks certain to miss Saturday's home encounter with Wigan, there is more positive news regarding Josh Morris.
Morris joined Billy Clarke on the Valley Parade pitch on Tuesday afternoon for a training session with assistant boss Steve Parkin and goalkeeper coach Lee Butler.
The pair have both been injured recently due to their own knee problems but Parkinson is hopeful that Morris' time on the sidelines could be about to end.
Parkinson continued: "Josh Morris and Billy Clarke took part in a really good session out on the pitch a few hours before the game.
"That is a good sign for us because they are two quality footballers.
"With Steven Davies getting injured now, we are definitely going to need them two back as soon as possible.
"Hopefully Josh will be involved on Saturday."
City supporters can watch the FULL post-match interview with Phil Parkinson on Bantams Player HD - please click HERE.