Bielik, who arrived from West Bromwich Albion, followed Lincoln midfielder Jack Moylan in joining Cardiff.
The Welsh club have also signed goalkeeper Nathan Trott on a permanent deal after his loan spell last season and re-signed Calum Scanlon on loan.
Bielik, a centre-back who can also operate in midfield, produced a promising performance in an entertaining game against the Blades.
The 28-year-old limped off in the closing stages but Cardiff are confident he was suffering with cramp rather than an injury.
“I thought he did a great debut, really good,” Barry-Murphy said.
“He has not played a lot so he was probably feeling the pace of the game I think throughout the first half, but in the second half I thought he showed his real quality and calmness and composure.
“I was slightly concerned when I saw him go down but I think it’s just pretty bad cramps, so hopefully he’ll be OK.”
