The frustration at the full-time whistle was magnified as Cambridge United had been reduced to 10 men with just over an hour played.
A moment of madness from Cambridge United's Liam O'Neil looked to hand the hosts the advantage they needed to turn to one point into three.
The Cambridge midfielder was shown a straight red card by referee Oliver Yates for a cynical challenge on Clayton Donaldson.
Bradford had created more chances and looked the better side until that point but failed to get going after gaining the man advantage.
The only clear-cut chance after the red card fell to Donaldson who was inches away from converting Daniel Devine's low cross.
City had lacked width for the majority of the afternoon, however the introduction of Sean Scannell on 75 minutes provided more threat on the wing.
Manager Gary Bowyer opted for a 4-3-3 formation with new recruits James Vaughan and Donaldson starting in the front trio.
It failed to have the desired effect as his front three were left without much support when they received the ball high up the pitch.
Bradford had 22 shots at goal but only three of those were on target as Cambridge held out for the one point.
When the hosts did get forward at pace they failed to move the ball quickly enough in the final third, allowing United to get enough bodies behind the ball.
The clash was the first time the clubs had met in league competition for over 25 years, the Bantams were held to a 1-1 draw by Cambridge on that occasion and the sides shared the spoils again in a feisty encounter.
City looked a much more cohesive unit at the back, something that will set them in good stead as the season wears on.
The clean sheet was a testament to the hard work put in by Bowyer's side during their pre-season campaign.
The Bantams only conceded five goals in seven pre-season games, three of which were against European Cup winners Liverpool FC.
Centre-backs Anthony O'Connor and new recruit Ben Richards-Everton marshalled the back-line well, with Cambridge prevented from creating any chances of note.
The visitors only had one shot on target in each half but never troubled Richard O'Donnell in the home goal.
Full-back Kelvin Mellor was able to find plenty of space on the right flank in the opening 45 minutes but was only utilised on a handful of occasions.
Newly-appointed captain Vaughan twice came close to opening the scoring; his first attempt was an audacious overhead kick that skimmed the top of the woodwork.
Bradford were roared on by a crowd of 14,810 - their highest opening-day attendance in the fourth tier - after a drive to reconnect with their supporter base during the off-season.
The draw didn't come due to a lack of effort on Bradford's part and the City faifthful applauded the home players as they left the pitch at full-time.
Meanwhile, the Bantams made history as they became the first English Football League club to wear heritage numbers on their shirts.
Bradford City: Mellor; Richards-Everton, O'Connor, Henley (Longridge 80); Palmer, Anderson (Devine 64), Gibson; Donaldson, Doyle (Scannell 75), Vaughan. Unused substitutes: Hornby, French, Wood, Colville.
Cambridge United: Mitov; Knoyle, Taylor, Taft, Jones (Dunk 67); Lambe (Maris 67), O'Neil, Lewis, Hannant; Dallas (Smith 63), Ibehre. Unused substitutes: Burton, Darling, Davies, Knowles.
Referee: Ollie Yates