Blades search for new keeper
Bunn, who has been at Bramall Lane all season, will return to Rovers to cover the absence of ex-Leeds and England keeper Paul Robinson who is out injured for the next month.
He played his final United game last night in the 3-0 victory over Blackpool and could make his Premier League debuut for Blackburn against Chelsea on Sunday.
Speed said: "Bunny has gone now. He has been recalled.
"We need to thank him for everything he has done. He has been fantastic.
"I am sure we will be looking to bring someone in."