Kevin Blackwell's side finished rock-bottom of League One and almost went out of business in May.
But after an exodus of players and a change in ownership, a new wave of optimism has swept over the club.
Jones told the Shakers' official website: "You walk into this place now and there is a massive difference in the club.
"The mood in the camp is very good, when you look back to the end of last season, it was all doom and gloom, but you come in now and people have their heads held high.
"There are massive changes being made, not just on the field, but there are a lot of things happening around the ground and the new owners are moving the club forward.
"The club was so close to going out of business, but you look around now and its exciting times for us all."
Bury made their first three signings of the summer on Thursday afternoon.
Left-back Gareth Roberts joined from Derby, with Euan Holden putting pen-to-paper on a permanent deal. Ashley Grimes completed the trio of arrivals, making the short move from Rochdale.