Stuart McCall's men bossed long periods of the game, but they failed to find the breakthrough against a well organised Town outfit.
City have now notched four clean sheets on the bounce and the Bradford boss was pleased with the performance if not the result.
The home side piled on the pressure from the start and striker Barry Conlon came close to putting them ahead after just eight minutes when he tried his luck with a left-foot volley.
The Irishman let fly from 20 yards, but his strike hit the inside of the post and rebounded to safety.
With Town's 20-goal striker Grant Holt seeing little of the ball early on it seemed only a matter of time before City opened the scoring, but things failed to go their way.
Full-back Luke O'Brien had a strong penalty shout waived away after he was sent tumbling in the Town box and in-form striker Michael Boulding wasted a great chance, when he shot straight at the keeper after good approach play by Paul McLaren and Conlon.
Just before the break centre-half Graeme Lee made a crucial block as Holt threatened to pull the trigger and the Town dangerman had a penalty claim of his own turned down just after the hour mark.
For all their possession and territory, City failed to test young keeper Luke Daniels enough after the interval and they were restricted to long-range shots and a few half chances as the game fizzled out.
Holt had a snapshot saved by Rhys Evans late on and Bradford's on-loan recruit Chris O' Grady failed to provide the spark up front when he made his debut off the bench with 15 minutes left.