Bradford, without leading goalscorer Nahki Wells who was transferred to neighbours Huddersfield this week, made a great start, taking the lead in the first minute through James Hanson.
Hanson got his head to a left-wing corner from skipper Gary Jones and, as the visitors' defence failed to clear, the ball came back to the tall striker, who stabbed it into the net just inside the near post.
But City equalised after 11 minutes when a long ball out of defence from Derrick Williams was headed on by Jay Emmanuel-Thomas into the path of Scott Wagstaff, who scored with an angled shot into the far corner from the edge of the penalty area.
The visitors took charge after their equaliser, but Bradford had a great chance to regain the lead a minute before the interval, only for Garry Thompson to fire across the face of goal with only goalkeeper Elliott Parish to beat.
Both sides hit the post in an exciting second half, Emmanuel-Thomas for Bristol City, substitute Jason Kennedy for Bradford, but neither team could force a winner.