Darby was given his marching orders less than twenty seconds into the second half at the Coral Windows Stadium following his second booking of the game.
Given the fact that the dismissal came as a result of two bookings, Darby will miss only the Ashton Gate fixture on Tuesday night.
Because the red card was due to two bookings though, it means City cannot look to appeal Darby's dismissal even if they wanted to.
After serving out his own suspension this Saturday, Gary Liddle will be available for the Bristol City fixture though.
Speaking about Darby's red card, Bantams boss Phil Parkinson said: "The Stephen Darby red card changes the game really because everything we said at half time just about went out the window. It obviously meant we had to re-jig the side.
"I didn't see the foul live as I was coming out of the tunnel at the time. Looking back at the incident though, I think it is a tough, tough call on Stephen.
"To get sent off for that is tough. The referee perhaps could have managed the situation better and given him a final warning.
"The first tackle is definitely a yellow but I just think the second incident could have been managed better."