The 24-year-old has impressed Kevin Blackwell in his loan stint so far, which was due to run out after the game versus West Brom on Saturday. He will play his football at Beautiful Downtown Bramall Lane until the end of 2009 after Blackburn allowed United to keep him for a further four months.
Bunn has had a good rapport with the fans since joining on loan and has kept two clean sheets in four appearances.
"We are indebted to Sam because we know he will have been concerned about leaving his own club short of cover," said Blades boss Kevin Blackwell.
"Getting Mark in for longer is a big relief considering the position we find ourselves in. He has settled, done well and his presence will maintain continuity instead of having to start all over again."