Lee Johnson's side dumped out Manchester United in the last round and will be hoping to pull off another shock with a trip to Wembley Stadium now in sight.
Here's how you can watch the game.
Date: Tuesday, January 9
Time: 7:45 p.m. GMT/2:45 p.m. ET
TV: Sky Sports Football (UK), ESPN 3 (USA)
The hosts will be huge favourites to secure victory on Tuesday night, as they remain unbeaten in the Premier League and are 15 points clear at the top of the table.
Guardiola has rotated his squad for the League Cup, using a blend of youngsters and fringe players, and they have been taken to penalties in the last two rounds.
Those results may give the Championship side hope, and they will also have confidence having already knocked out four Premier League teams in their run so far.
They will also be backed by the biggest away following in the Etihad Stadium's history, per the club's head of media Adam Baker:
The Robins go into the game after being knocked out of the FA Cup by Watford 3-0 on Saturday, although they did put out a much-changed side with one eye on Tuesday's game.
Korey Smith was the Ashton Gate team's hero against United, and he was taken off at half-time against the Hornets, but the substitution was only precautionary, assistant head coach Dean Holden confirmed:
Manchester City also made changes for their 4-1 FA Cup third-round win on Saturday, but it was still a strong team that came from behind to beat Burnley, with Sergio Aguero (twice), Leroy Sane and Bernardo Silva on target.
Much may depend on what kind of team Guardiola puts out for this one, but City also travel to Anfield to take on Liverpool on Sunday. Consequently, they could continue with an inexperienced lineup, which may give Johnson's side hope of another shock.