Bulls 10 Warrington 23
Mick Potter's men slipped to a contentious third successive home defeat of the season but only after a vastly-improved display in which they matched leaders Warrington for long periods.
Bulls hooker Matt Diskin put the hosts ahead with a close-range score in the fifth minute before a series of controversial decisions from the officials went Warrington's way.
Chris Riley grounded a pass from Brett Hodgson which clearly looked forward and Bradford then had tries from Jarrod Sammut and Michael Platt disallowed by the video referee.
Mickey Higham sneaked over the line for Tony Smith's side shortly before half-time and two minutes after the break Ryan Atkins, released by the Bulls in 2006, raced the length of the field to score.
Trent Waterhouse claimed a fourth try for the visitors in the 61st minute and, although the spirited Bulls replied through Jason Crookes' clinical score, Warrington confirmed victory with a late drop-goal from Lee Briers.