The Latics will be hot favourites to reach the quarter-finals for the second time in three seasons, with their opponents playing in the bottom tier of the Football League for a sixth successive campaign.
But Bradford have made a good start to the season, winning seven of their opening 15 league games, while their cup scalps have included Notts County and Watford.
Midfielder Jones told wiganlatics.co.uk: "I don't think we can complain about how we've performed in the last two rounds.
"We'll go into this one as favourites but we're expecting a really tough game because it's a chance of an upset for them, and obviously they've done well to get to this stage.
"I'm sure they'll pose a lot of problems, different problems than we face on a Saturday. And we don't know what team the manager will put out.
"In the previous rounds, players who haven't started in the league as much have been coming in and playing in the cup so if he does the same you don't know how the team's going to come together. But I think we've got a good chance of going far in this competition."
Jones has not played since the previous round against West Ham a month ago, when Wigan won 4-1, while strikers Mauro Boselli and Callum McManaman have also had little chance to impress in the Barclays Premier League.
All three are likely to be given another run-out but boss Roberto Martinez will not be able to call on winger Ryo Miyaichi, who is still struggling with a groin problem.
The manager is hoping home comforts will help Wigan in their quest to match their run of two seasons ago, when they eventually lost to Arsenal in the last eight.
Since that night at the Emirates, Wigan have played seven ties in the League and FA Cups, only one of which was at home, and that was a replay.
Wigan gave themselves some breathing space in the Premier League with victory over West Ham on Saturday, and Martinez has now turned his focus to further cup progress.
He said: "Every game is a big game now. Getting into the final eight is a fantastic prize for Bradford and for ourselves. We're going to get 5,000 supporters from Bradford and that's going to make it a big game.
"We're really looking forward to it. We've had two fantastic performances already in that cup and now we need to get the same standard at home. It's the first time we've had a cup game at home in the last two years and we need to make the most of it."
