Danny Wilson's United continued the unbeaten start to the season but were held to a draw at Bramall Lane on Saturday.
The Blades handed debuts to Darryl Westlake, Paul Gallagher and Dave Kitson but were unable to maintain the winning record at home.
Nick Blackman gave the Blades an early lead but Bury's Peter Sweeney levelled just two minutes later.
Gallagher and Westlake made their debuts for United, replacing the suspended duo of Doyle and Flynn, who began their three-match bans. Collins donned the captain's armband, whilst Kitson was on the bench for the first time.
Kick-off, after Blades supporters had bid a fond farewell to Nick Montgomery, saw Gallagher line up on the left side of midfield with Westlake, possibly surprisingly, partnering McDonald in the middle of the park.
The first action was at the Kop end, which United were defending. Maguire saved McMahon's blushes by making a fine tackle on Marshall and then Craig Jones fired straight at Howard. The Blades, though, needed just one attack to open the scoring. Gallagher's delivery was inch-perfect to beat the Bury defence and BLACKMAN read it well, taking a controlling touch before smashing past Carson.
The goalscorer almost repeated the feat within seconds, but Bury soon levelled. McAllister was punished for a foul on Marshall on the edge of the box and SWEENEY's left-footed free-kick flew over the wall and found the net, despite Howard getting a hand on it.
Cofie got on the end of a Blackman delivery, but could not direct the ball towards goal, whilst a cross by McMahon saw Maguire's powerful header saved by Carson on the half hour. Blackman also fired just wide, but despite United creating the better chances, the remainder of the half was insignificant with just a number of refereeing decisions forcing the crowd to comment. Just before the interval a header from Craig Jones needed tipped around the post, which Howard dealt with.
Once more a few decisions from the officials went against United in early stages of the half, whilst Wilson made a change just seven minutes after the restart, Cresswell taking the place of Cofie. McAllister, who had been moved into central midfield with Westlake switching to the right, fired over.
McDonald was booked for a frustrated challenge on Marshall and soon after the Blades midfielder threaded a ball through for Blackman, whose shot was deflected wide. Bury's first chance of the second half was a good one, Craig Jones supplied Cullen, who showed good control before volleying just wide.
An impressive Blades move, involving McAllister and Cresswell, resulted in Blackman's shot being parried away by Carson, whilst the home fans were praising the referee on 67 minutes when McDonald, already booked, fouled Sweeney - after a lengthy chat the midfielder did not receive further sanctions. Ironically, Sodje was booked for voicing his protests and he also survived moments later, despite clattering Cresswell.
Late on, with Bury slowing down the action at every opportunity, United forced the visitors back. Twice in the space of five minutes Blackman found room after playing one-twos but on both occasions his shots were saved by Carson, who also provided a number of valuable punches away.
Kitson was introduced for his debut in the final ten minutes, whilst there was a hearts-in-the-mouth moment on 84 minutes when John-Lewis flicked on and Cullen looked in the clear before McMahon made a last-ditch tackle - Bury were also denied in their penalty shouts.
The annoucement of four minutes of added time coincided with an unmarked Cullen heading over a great chance to win it for the visitors, whilst Blackman also fired into the side-netting before referee Hooper blew the final whistle to signal a draw.
Blades: Howard, Westlake (Kitson 83), Maguire, Hill, Blackman, McDonald, Collins, McAllister, Cofie (Cresswell 52), Gallagher, McMahon.
Unused: Miller, Harriott, Long, McFadzean, Williams.
Bury: Carson, Skarz, Lockwood, Sweeney, Schumacher, C. Jones, Marshall, Sodje (Hughes 75), Cullen (Byrne 90), A. Jones, Hopper (John-Lewis 68).
Unused: Carrington, Elford-Alliyu, Dibble, Pratt.