Suspension and injury respectively will also rule both midfielders out of the return leg on Sunday and the final at Wembley - should Gary Rowett's side reach the May 18 showpiece.
Bell received his second red card of the season during the league meeting with the Bantams 11 days ago and will serve the second game of his four-match ban.
Dyer suffered ankle ligament damage in that 1-0 defeat in West Yorkshire and he faces up to six weeks on the sidelines.
It looks like either John McGrath, who got the nod for the final game of the campaign at home to Gillingham at the weekend, or Lee Fowler will play alongside Robbie Weir in central midfield, although Brewers boss Rowett has not ruled out a change in formation.
"We've got lots of options," he said. "We could play extra players in there, or we've got an opportunity to do things differently with the formation. We can drop Zander Diamond into the back four to make it a back five.
"There are lots of things we can do but the key is we don't want to tinker too much."