Oakwell academy product Rose, 20, joined his former Reds boss David Flitcroft at the League Two club, initially on loan on Friday then permanently on Monday.
He scored in both of the Shakers' matches this week to take his career tally to seven in four starts. Reds chief executive Ben Mansford has confirmed that the fee Bury paid is almost the same as the amount Barnsley paid up front for Winnall, which was a six figure sum but is believed to be smaller than the £250,000 reported by Scunthorpe.
Winnall's deal could rise to far more than Rose's depending on how the Reds do this season but the Oakwell club do have a significant sell-on clause should Rose ever leave Bury.
"We received what we thought was a very good offer for a player who had only played a handful of first team games," Mansford told the Chronicle.
"It's very, very similar to the initial fee we paid for Sam Winnall."
Mansford admits that the quality of the offer was offset by the board's reluctance to sell a homegrown player so they let a tearful Rose make the final decision. The chief executive said: "We didn't want to let one of our own go but it was a deal that worked for us. None of myself, the manager, the owner or the chairman could decide what to do so we gave Danny the choice. He was very upset, as were his parents, but he decided to leave. "We wanted him to stay but we couldn't guarantee him first team football."
Rose started the first game of Barnsley's season but has since slipped behind new signings Leroy Lita, Sam Winnall and Kane Hemmings. Reds boss Danny Wilson said: "Danny is a great lad and I'm delighted he made the decision. We left it to him and he said that he wanted to leave and play football. "It's a great move and he'll get consistent football which is what he needs. "We talk about players who are 20 or 21 and call them young lads but, when I was that age, I'd played 200 games."
Rose – who played 18 times for Barnsley – added to the three goals he got in six substitute appearances while on loan with the Shakers last season when he came off the bench to net and secure a 2-0 win at Hartlepool on Saturday. He then started at Luton on Tuesday and bagged again in a 1-1 draw. Bury chief executive Glenn Thomas has contacted Mansford to ask about Rose every week since they met at a conference in May in what he called a 'tireless objective.'
Flitcroft, who was the manager of Barnsley when Rose got his two Reds goals, said: "This has been a big chase for us and we are obviously delighted to finally get the deal done. The fans love him, the players love him and we have really worked hard on this one. He's a fantastic kid to have around the place and we saw on Saturday just what it means to him.
"It's been difficult for Danny because he is Barnsley born and bred. It's been difficult for his family because he wanted desperately to do well for Barnsley Football Club. "He has seen other players develop with their setup and he wanted it. He's had to finish one chapter at Barnsley to move on to another chapter with Bury."
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