In a game of few openings, Capital One Cup semi-finalists Bradford had the best chance to take the three points when striker James Hanson missed a glorious opportunity 10 minutes from time, heading weakly at Barry Roche from six yards when he looked sure to score.
Roche was Morecambe's hero earlier in the half with an excellent stop from a Hanson header before saving sharply to keep out a long-range Nahki Wells effort.
The Bantams always looked the more likely side to win the game and in a poor first half went closest to breaking the deadlock through Hanson, who reacted sharply in the box to volley a right-wing cross goalwards but, again, Roche produced a good save with his legs.
After a slow start Morecambe began to produce some pressure, with Stewart Drummond and Lewis Alessandra both volleying well over the bar from distance, but Matt Duke's goal remained largely untroubled.
The home side's best chance came in the closing moments when substitute Richard Brodie headed an Alessandra free-kick over.