Bulls have been drawn at home to Warrington Wolves in this evening's Tetley's Challenge Cup quarter-final draw, while Keighley Cougars will visit Widnes Vikings.
Francis Cummins' side produced a fine comeback to beat Catalan Dragons 33-20 in the last round and will look to take advantage of another home tie at Odsal to progress further, though 2012 winners Wolves will prove tough opposition.
Cougars, who were hoping to land a plum tie against a big Super League club after beating Swinton in the last round, will travel to Widnes Vikings in a repeat of the 1937 Wembley final.
Other ties see Leeds Rhinos at home to Championship club Leigh Centurions, while holders Wigan Warriors are at home to Castleford Tigers.
Matches will be played on the weekend of June 7-8.