Bradford made a great start with an early goal from James Hanson, who got his head to a left-wing corner from skipper Gary Jones after the visitors had failed to clear.
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 just goalkeeper Elliott Parish to beat.
Both sides hit the post with long range efforts in an exciting second half, Emmanuel-Thomas for Bristol City and Jones for Bradford, while Parish dived full length to keep out a goal-bound header from defender Rory McArdle.
The result extended the visitors' unbeaten run to five matches and Steve Cotterill, who joined the club as manager in early December, said: "It was a very tight game.
"After a sloppy start, I thought we were by far the better team in the first half and it was like attack against defence, but Bradford came into it in the second half.
"They play direct with a lot of balls aimed for James Hanson and they are a handful.
"We needed to get a second goal and if we had done that we would have won the game.
"We were not at the races in the first five minutes, but we recovered from that and ended up dominating the game.
"Both sides hit the post with wonderful strikes that could have won the game."
Bristol City began the day third from the bottom with only four wins from 23 matches, but Cotterill is confident of climbing the table.
"I think we are playing very well and we will get better with time," he said.
"Something has not been right at the club for a number of seasons so that decline has got to stop.
"We have got to set ourselves new standards and we are trying to do that."