Striker Bednar recovered from a groin problem to make a second-half substitute appearance against Blackpool on Saturday but has then picked up a thigh injury in training on Monday and is back in the treatment room.
Versatile on-loan man Reid sustained a groin injury in the 3-2 triumph at the weekend and also misses out, while winger Jerome Thomas has failed to recover from his hamstring injury.
Ishmael Miller scored against Pool in what was his first start for 15 months but he was later replaced by Bednar due to a hamstring problem of his own, but he is hopeful of being available.
Fellow forward Luke Moore may also overcomes illness in time to be involved at the Liberty Stadium but Gonzalo Jara (broken metatarsal) remains out for the rest of the season.
Albion will be bidding to become only the second team after Nottingham Forest to beat fourth-placed Swansea in 15 league attempts.