The 25-year-old Clark signed a two-year contract with the Scottish Championship club after making only four appearances in two months with the League One side.
The Shakers last week signed James Vaughan from Birmingham City.
And manager David Flitcroft told the Scot that it would further limit his chances of a starting place.
Clark will now work under father Sandy, who is Allan Johnston's assistant at East End Park, having previously played for the pair at Queen of the South.
Having come through the youth ranks at Aberdeen, Clark moved on to Peterhead before joining Queens, for whom he scored 39 goals in 79 appearances.
Clark moved to Rangers in 2013 and, although he never became a regular starter, he helped the Glasgow club win League One and the Championship.
After signing a two-year contract, he played in four of Bury's first five matches of the season but was on the bench against Walsall and then left out of the squad against Morecambe.
Herron, who joined Blackpool last summer after leaving Celtic, joins the Pars until January.
The 22-year-old has made 20 appearances for the League Two club, 11 of them as a substitute.
Dunfermline Athletic have signed former Rangers striker Nicky Clark from Bury and signed midfielder John Herron on loan from Blackpool.