The Bantams made headlines around the world last season after beating both Chelsea and Sunderland en route to the quarter-finals.
However, before taking on the Premier League duo, City had to overcome a tricky trip to FC Halifax Town in the first round and then a home tie against Dartford.
Manager Phil Parkinson said: “The lads know from last season the big rewards that can be earned by getting through the early rounds.
“We beat Halifax and Dartford to reach the third round. We knew we had been in a game after both of those, and in particular Halifax. We had known what to expect and although we deserved to go through, it wasn’t easy.
“The exposure and glamour that came from Chelsea, Sunderland and reaching the quarter-finals was only possible because of the hard work everyone put in against Halifax and Dartford.
“We will need to work just as hard against Aldershot.”
The Shots sit 12th in the National League but Parkinson has warned his Bantams side, who moved up to ninth in League Two during midweek, against complacency.
He added: “Aldershot are quite a young, athletic team. I have watched a few DVDs of their games and we had someone at the Southport game last week. We have sat the lads down and talked them through the way that Aldershot play.
“It will be one of those days when our attitude has to be spot on. We do not want to be the team making the headlines on Monday morning, as that will mean we have gone out of the Cup.
“The players are fully aware of that and I am expecting a professional performance from us all.”