A strong second half showing from opponents Swindon Town condemned City to defeat on the opening day of the new 2015/2016 campaign.
A hat-trick from the lively Nathan Byrne after the restart and a fourth goal from the boot of Jonathan Obika made it a difficult afternoon for Phil Parkinson's men after such a promising opening to the game.
City found themselves deservedly in the lead at half time thanks to Josh Morris' first goal for the Bantams only five minutes into his full debut for the club.
Parkinson's side could have been further in front at the break but Billy Clarke saw a penalty saved by home shot-stopper Lawrence Virgouroux. The Irish striker also came agonisingly close with a fabulous lob from distance that bounced narrowly wide.
The Bantams will have been aiming to continue where they left off in the second period but a forceful response from Swindon, inspired by the presence of Byrne, saw the opening day points remain in Wiltshire.
In beautiful August sunshine, City, kitted out in their new all-black away strip, had begun the game in confident fashion, and it didn't take them long to grab an advantage.
Following Stephen Darby's long throw-in down the line, James Hanson headed the ball into the path of Billy Knott, who in turn fed Tony McMahon.
McMahon spotted Morris in space across the edge of the area and new Bantams midfielder proceeded to lash the ball home into the top corner with a fine first time strike.
Morris was at the heart of the action again with less than 20 minutes on the clock as City won their first penalty since last September.
Morris drew a challenge inside the box from Nathan Thompson and referee Mr Stephen Martin had no hesitation in pointing to the spot.
Clarke took responsibility for the kick but Swindon shot-stopper Lawrence Vigouroux guessed the right way and pushed his penalty around the post.
On the half hour mark, Clarke had the opportunity to make amends in spectacular fashion, however, when he robbed Jordan Turnbull of the ball just inside Swindon's own half.
With Vigouroux off his line, Clarke sent an ambitious lob over his head - only to see the ball drop agonisingly just wide of the post.
As City continued to look strong in the opening period, Billy Knott came within mere inches of tapping in Morris' shot across goal before Christopher Routis saw a header from a corner hacked clear of the line.
Unfortunately for City though, the start of the second period saw a change in the flow of the game as the hosts started to impose themselves more on the match.
Swindon equalised with less than six minutes on the clock after the restart, although the goal seemed to have a touch of fortune about it.
Byrne looked to feed the ball into an area with a strike using the outside of his boot. The effort seemed to be going towards Obika but the striker moved out of the way at the last moment, unsighting Ben Williams in the process as the ball nestled into the far corner.
Swindon's comeback in the match was complete just past the hour mark when Kevin Stewart led a dangerous home counter-attack before slotting in Byrne, who slide the ball low past Williams.
City, who had brought on Steven Davies by this stage, were struggling to come to terms with Swindon's upturn in their performance, and they were powerless to prevent Byrne from grabbing his hat-trick just seven minutes later with an eye-catching third.
After picking up the ball outside City's box, Byrne surged into the penalty box, driving past three Bradford players at the same time, before drilling in a low shot between Williams' legs.
Third sadly became four for Swindon shortly afterwards when Obika latched onto Turnbull's pace, held off Nathan Clarke and fired past Williams from just inside the area.
A shell-shocked City introduced Paul Anderson and Mark Marshall in the action later in the half but the damage had been done by that stage and Parkinson's men were left to lick their wounds on the long coach journey home.