City led 2-0 through Dean Windass after 23 minutes but Rovers came surging back to turn the tables by scoring three goals themselves.
The home side had skipper Graeme Lee sent off for a second bookable offence in the 82nd minute and Bridge-Wilkinson brought the curtain down on a pulsating derby clash when he equalised from the resulting free-kick.
It was Bradford who made the running at the start and they rocked Rovers with a goal after just 40 seconds.
Speed merchant Jermaine Johnson raced through on the right to hammer a low shot which Jan Budtz could only parry and Windass followed up to fire home from close range.
Doncaster piled on the pressure in a bid to fight back but Paul Heffernan twice had goalbound efforts blocked before Lewis Guy had a header saved by Donovan Ricketts.
Windass made it 2-0 in the 23rd minute with a superb goal when he sent a bullet-like header powering into the back of the net after beating Adam Lockwood in the air to meet a right-wing cross from Nathan Doyle.
Doncaster seemed undaunted and Heffernan was unlucky when he had a thumping volley deflected over the bar three minutes later.
The home side hit back just before the interval following great play by Heffernan and Guy which led to Paul Green forcing the ball over the line.
City started the second half as they did the first but Doncaster defended better this time and they scored again in the 51st minute following a free-kick.
Brian Stock floated the ball to the near post where Green beat everyone to send a glancing header into the back of the net.
Remarkably the home side went in front a couple of minutes later with a tremendous goal from James Coppinger who turned on a six pence to hammer a cracking effort home off the underside of the crossbar.
It had been a remarkable transformation but there was a twist in the tale when skipper Lee was given his marching orders in the 82nd minute after bringing down Windass just outside the box.
Bridge-Wilkinson hammered home the resulting free-kick to set the seal on a match that had provided five-star entertainment.