An outstanding second-half save from Chesterfield's on-loan keeper Marton Fulop denied Andy Cooke what would have almost certainly been a winning goal.
But apart from that, there were few other clear openings with both defences staying on top for much of a disappointing contest.
Bradford recalled winger Nicky Summerbee after a two-game absence but he failed to produce the moment of quality that could have unlocked the home defence.
Summerbee was eventually substituted 13 minutes form the end and there was little else in the closing stages of the game that suggested Bradford would get the win they desperately needed.
It might have been different if Steven Schumacher had enjoyed better luck with two first-half efforts.
On both occasions Chesterfield left him unmarked on the right hand edge of the area at corners and they nearly paid the price.
His first low shot was deflected by Dean Windass into the arms of Fulop but his second whistled just past the post with the keeper beaten.
Chesterfield created little and Paul Henderson did not have a serious save to make in the game.
Fulop showed why Spurs rate him highly in the 61st minute when he flew to his right to palm away a Cooke header that looked destined to find the net.
Cooke also headed powerfully at the Hungarian keeper shortly before he was replaced and Chesterfield's best effort came in the 69th minute from a long throw.
The ball was flicked on by Steve Blatherwick but his central defensive partner Ian Evatt could not force the ball home.