Bristol City are locked in the relegation battle and, unless Bradford can turn draws into wins, they may find themselves joining them.
The visitors were quickest out of the blocks and could have been in front in the first minute but Dave Cotterill blazed a good chance over. Just a minute later Steve Brooker forced a fine save from Donovan Ricketts as Bradford struggled to get any sort of stranglehold on the game.
Before they had forced a save of note from Adriano Basso in the Robins goal, they found themselves behind on 16 minutes.
Scott Murray exchanged clever passes with captain Brooker who cut inside Darren Holloway before firing past Ricketts from the edge of the area to give the visitors a deserved lead.
Bradford briefly threatened a fightback when Basso was forced into an acrobatic save to deny Damion Stewart his first goal for the club.
That was the closest Bradford were to come to scoring in a tepid first half. But the Bantams came out fired up after the break and were soon on level terms when substitute Joe Colbeck's surging run down the right forced a corner.
Marc Bridge-Wilkinson's centre was cleared as far as Darren Holloway whose cross found Wetherall unmarked at the far post and the City skipper nodded home the equaliser on 57 minutes.
From then on it was virtually all Bradford as the home side went hunting for a winner which should have been supplied by Dean Windass.
Bradford's leading scorer was playing in his last match before starting a five-match ban, and was desperate to sign off in style.
He had the perfect chance with just 15 minutes left. Bridge-Wilkinson's cross found him all alone at the far post with time to pick his spot. But he opted for power instead of placement and put his shot too close to Basso who produced another fine stop.
Bradford worked hard to force a winner but it was the visitors that nearly nicked it when Mark McCammon's header was cleared off the line.