Nedum Onuoha cannot play against Manchester City in the Premier League on Sunday because he is only on loan from the Citizens.
According to media reports, Bruce is now likely to play either Anton Ferdinand or Phil Bardsley at right-back, where Egyptian wide man Ahmed Elmohamady used to playing.
Elmohamady can be deployed on the left flank too.
"It was a big problem for me last year getting a settled back four and we are already suffering this season as well," Bruce said.
"There is one Premier League goalkeeper out injured at the moment and that is Craig Gordon and we have had a different back four in every game we have played.
"Nedum, who has done really well for us so far, cannot play tomorrow, so we will have another one. It is not just the back four, though.
"We have made huge changes to the team so it needs time to settle down, especially as some of the new players have not even played in England before."