Victory was especially sweet for manager Alan Knill - who has now guided his side to five victories in the nine games he has been in charge - as it was against his former club.
Knill managed the Millers for a two-year spell between 2005 and 2007 so it came as little surprise that the Gigg Lane gaffer was delighted with his side's victory as they continue to battle away from the relegation zone.
As early as the tenth minute, Bishop forced a point-blank save from former Bury keeper Andy Warrington, but six minutes later the striker gave the home team a deserved lead.
Pablo Mills tried his luck with a 35-yard thunderbolt, but the midfielder was agonisingly unlucky as the ball flew wide at the left-hand post.
At the other end, Glynn Hurst fired into the side-netting, before Mills went close with a half-volley and a right-foot curler.
But the home team were indebted to their keeper Darren Randolph who, with a superb save, tipped Peter Holmes' header past his left-hand post.
Elliott Bennett set up Bishop eight minutes into the second half, but the centre-forward's left-foot shot was straight at Warrington.
Chris O'Grady saw a shot saved by Randolph on the line, before Adams fired over from just outside the penalty area.
But Bury gave themselves welcome breathing space when Bishop raced clear and slotted underneath Warrington to make it 2-0.
The striker latched onto a mis-timed backward header from Rotherham defender Marc Joseph, before firing into the far corner.
Victory was secured when Adams beat Warrington with a left-foot strike in the 66th minute, although the keeper should have done better as the ball bobbled up tamely over his body into the net and the majority of a disgruntled and freezing cold Millers contingent headed for the exits.