Gavin Tomlin cancelled out Zac Thompson's opener for the Shakers to ensure the game went to spot kicks.
And that enabled Bentley to centre stage as he kept out penalties from David Worrall and Mark Hughes to send Blues through to the third round.
Up until then, both sides struggled to deal with a difficult pitch in freezing conditions.
However, with 59 minutes on the clock, the Shakers went in front, following a rare mistake from Ryan Cresswell.
The towering Shrimpers centre-back gave the ball away poorly in his own penalty area and that enabled Andy Bishop to tee up Thompson and he made no mistake with an assured finish from 12 yards.
But Bury were in front for just four minutes as Tomlin headed Blues back level.
The in-form forward was picked out by an excellent right wing cross from Sean Clohessy at the near post and nodded the ball in to the bottom left hand corner of the net.