Bantams centre-half Reece Burke went closest to breaking the deadlock but his second-half header went just wide.
Home midfielder Danny Pugh forced keeper Ben Williams into a good save, while John O'Sullivan and Andrew Tutte also tested him.
It was the third consecutive 0-0 draw between the two sides, including an FA Cup replay.
Bradford moved to within three points of the League One play-off places after a goalless draw at Bury.