The Jamaican international winger scored the only goal - from the penalty spot - when Bradford won 1-0 at Gigg Lane on November 2 and also scored the winner in the return match at Valley Parade.
On-loan midfield player Tom Adeyemi crossed from the right for Daley to score with a superb right-foot volley from 10 yards in first-half stoppage time.
Bradford missed chances to increase their lead in a thrilling second-half, the easiest one falling to midfield player David Syers after striker Gareth Evans' cross had left him unmarked at the far post in the 58th minute while Evans twice shot wide when well placed.
Bury, who made the early running might have gone in front in the fourth minute when Ryan Lowe saw his shot blocked on the line by goalkeeper Lenny Pidgeley.
Then, in the second-half, Pidgeley fumbled Lowe's shot and then Micheal Jones shot wide from the edge of the penalty area. Bury also applied more pressure late in the game, but Bradford's defence held firm.