Former Nigeria international Sodje netted with a 50th minute bullet header to cancel out David Buchanan's earlier own goal to make sure of maximum points.
And then it was left striker Bishop to make sure of the points from the penalty spot after Ben Wright had needlessly tugged Paul Scott's shirt in his own box.
Andy Morrell was also on target for Alan Knill's side, who leapfrogged Wycombe Wanderers and maintained the pressure on leaders Bradford City.
Morrell gave the hosts a deserved 30th minute lead when he headed in from a Michael Jones corner, but Buchanan unluckily deflected a Janos Kovacs corner into his own net to give the visitors hope.
But Knill's determined charges were the brighter of the two sides in the second half and, after Bishop saw a close-range header cleared off the line by Scott Kerr, Sodje headed in a Brian Barry-Murphy corner.
And it got even better for the Lancashire side as Bishop made no mistake with his spot-kick to stretch the club's recent unbeaten run of five matches.
As early as fourth minute, Bishop fired wide from an acute angle, before Kovacs tested Bury keeper Wayne Brown with a fierce left-foot free-kick from distance at the other end.
Kovacs fired over before Morrell opened the scoring, but Buchanan deflected into his own net to make matters all square.
The restart saw Lenell John-Lewis fire wide from the edge of the box, but the home side quickly stamped their authority on proceedings.
Bishop had his header cleared off the line, before the striker scored.
Elliott Bennett fired over with a right-foot shot after a quick counter-attack, before Bishop secured the points with his cool penalty strike.