City are scheduled to travel to the JD Stadium on the weekend of 8/9/10/11 January 2016 following Monday's draw.
City's trip to Bury means that the club's scheduled Sky Bet League 1 home fixture with Barnsley (Saturday 9 January 2016) will now have to be rearranged.
Phil Parkinson's men booked their place in the third round on Sunday with a 4-0 win over Chesham United.
On the same day, Bury also secured their progress into the next round of the FA Cup with a single-goal win at Lancashire neighbours Rochdale.
City and Bury have met once already this season, with Parkinson's side coming out on top 2-1 in a League 1 fixture at the Coral Windows Stadium.
Parkinson actually made his professional debut as a player for Bury back in 1988. The City chief spent four years at Gigg Lane before leaving for Reading in 1992.
City's Head Physio Matt Barrass also featured for Bury during his playing career.
The Bantams' previous match at Bury came just over five years ago when an Omar Daley first half penalty gave City a 1-0 win over the Shakers.
Match ticket details for this tie will be announced in due course.