Beaten in their last eight games and bottom of League One, Bristol cut admission prices by £5 to hold on to their crowd.
Just under 9,000 turned up but their misery continued as a late own goal by Louis Carey saw Bradford scrape to a fourth away win.
A cross from substitute Tom Kearney was turned in by the centre-back off a post.
It was Bradford's first win in the league since September and their first league goal for 440 minutes.
But the relief for their 150 travelling fans was put on ice as the visitors had to survive a hectic finish including a bizarre indirect free-kick from 12 yards that was deflected away.
The start was held up by 20 minutes with Bradford fans delayed by an accident on the M5.
Bristol though might have gone ahead on two minutes when Matt Heywood went up for a corner and Bradford keeper Donovan Ricketts and his defenders just managed to scramble the ball away.
Bradford were in trouble more than once as home defenders pressed forward for set pieces and twice Carey came close to opening them up.
But Bristol were not giving enough support to their one dangerous striker Stephen Brooker.
He was left to do too much of his own running as his partner Marcus Stewart, being watched by Plymouth Argyle, failed to make any impression.
He was replaced on the hour by a non-contract striker Bas Savage who recently joined from Coventry.
Bradford were constantly pumped long balls up for veteran Dean Windass but he was always well controlled by Carey.
There was more threat from the long range free-kicks of Marc Bridge-Wilkinson but it was Bristol who often looked more likely to score.
Their best chance came from a 45 yard free-kick from the left by Luke Wilkshire.
As Carey ran in to challenge the keeper the ball broke to David Cotterill but his first-time shot clipped the far post.