Witt claimed a try, four conversions and a drop-goal as the Broncos claimed a quarter-final spot for the second consecutive season. Matt Cook, Kieran Dixon and Scott Wheeldon also crossed for the hosts.
Bradford had opened the scoring through Jarrod Sammut, while Nick Scruton and Elliot Kear both went over late on.
Sheffield Eagles are through to the last eight of the Tetley's Challenge Cup after beating Championship rivals Halifax 28-12 in the fifth-round tie at the Don Valley Stadium.
The Eagles, who won the Cup at Wembley in 1998, raced into a 10-0 lead after nine minutes thanks to tries from full-back Quentin Laulu-Togagae and centre Tom Armstrong as well as a goal from Dominic Brambani, before Halifax centre Steve Tyrer pulled two points back with a penalty on the stroke of half-time.
But there was no way back after Laulu-Togagae went over for his second try 12 minutes into the second half, and although Rob Worrincy gave the visitors hope with a try on the hour and Callum Casey also scored, Sheffield added further tries through Scott Turner and Menzie Yere, with Brambani kicking his fourth goal.
England international Gareth Ellis made his mark on his second appearance for Hull to help them secure a comfortable passage through to the quarter-finals of the Tetley's Challenge Cup with a 24-6 win over Wakefield.
The 32-year-old second rower eased himself back into Super League with a low-key debut for the Black and Whites a week ago but rolled the years back with a superb performance as Hull clinically disposed of the visitors in their fifth-round tie at the KC Stadium.
Ellis, who was at the heart of a tremendous defensive effort and who tormented the Wildcats with clever offloads capped his display with his first try for the club while long-serving centre Kirk Yeaman scored his 150th, adding to two scores from Jay Pitts. Ali Lauitiiti replied with Wakefield's only score.