Bunn, who has been on loan at Bramall Lane since the start of the season, has been one of the mainstays in the United team this season, but will return to Ewood Park on Wednesday to cover the absence of injured number one Paul Robinson.
United coach Gary Speed said: "Bunny has gone now. 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."