City made the brighter start. Tom Kearney tried his luck with a shot from 20 yards after only two minutes. However, he could not keep it on target.
Steve Kabba, Grimsby's on-loan signing from Crystal Palace, had a chance to punish City but he failed to make them pay, hitting a weak effort wide.
Terry Cooke should have done better for the Mariners after 15 minutes when he cut inside from the by-line to line up a shot from ten yards.
But after doing all the hard work he let himself down with a poor shot which drifted past the near post. Stuart Campbell then tested City keeper Aiden Davison with a 12-yard strike.
Grimsby at that point had the edge but they suffered a blow when their other loan signing veteran striker Robert Taylor limped off with a calf strain on 19 minutes.
City were struggling to break down a well organised Grimsby defence but the home side almost opened the scoring after 34 minutes.
Danny Cadamarteri laid the ball into the path of Paul Evans who unleashed a 14-yard shot.
Unfortunately for Bradford, keeper Danny Coyne was more than equal to it, tipping the ball round the post for a corner.
Cadamarteri was again in the thick of the action a short time later. But he saw his powerful shot blocked after making a surging run towards the penalty box.
Kabba then used his pace to set himself up but he screwed his shot wide.
But it was Bradford who ended the half on a strong note. Ashley Ward was unlucky to see his angled header drift past the far post before Cadamarteri shrugged off a couple of players before drilling a low shot past the keeper's right-hand post.
Two minutes after the restart, player manager Paul Groves almost stretched City with a powerful header when he met Tony Gallimore's cross at the back post. But his header went wide and the chance was gone.
City threw on on-loan striker Michael Proctor at 60 minutes, replacing Kearney but the 21-year-old, who had joined City from Sunderland on a one-month deal, looked out of his depth on his debut.
Ward should have done much better when his weak header wobbled into the keeper's arms.
After 75 minutes Cooke curled a fine free kick from 25 yards but Davison always had his eyes on the ball and made a comfortable save.
Bradford could have wrapped up all three points in the dying minutes. Evans cracked a low drive off target before Michael Standing hit a stunning 30-yard drive which needed a superb save by Coyne to keep it out.
Speaking after the game Bantams boss Nicky Law said: "We are very disappointed. I know it's frustrating. It's frustrating for everybody.
"We have just got to keep plugging away and hopefully we will turn the corner."