City manager Phil Parkinson and O's assistat boss Kevin Nugent were sent off at half-time following an altercation in the tunnel leading to the dressing room.
The row broke out when the home side felt they were denied a penalty in the final minute of first-half added time, Dean Cox's shot struck the arm of a visiting defender, but referee David Phillips, surrounded by irate Orient players, insisted he had already blown for the interval.
The altercation continued down in the tunnel and Parkinson and Nugent saw red.
The goal came against the run of play after Orient had forged three good chances.
Kevin Lisbie, Moses Odubajo and Cox had all gone close before Bantams goalkeeper Jon McLaughlin pulled off the best save of the first-half when he dived to keep out a shot from Scott Cuthbert.
The home side though were undone by a set-piece when Gary Jones delivered a corner from the left and former Orient youth-team player Mclean, unmarked at the far post, drove the ball into the roof of the net.
After the break the home side enjoyed much of the possession, but showed little in the way of inventive flair and it was the Bantams who came closest to scoring when substitute Garry Thompson was denied by the outstretched feet of goalkeeper Jamie Jones.