Keighley came out of special measures a month ago following a change of ownership and the home derby will revive memories of the glory days of Cougarmania in the early Nineties.
The draw produced four other all-Yorkshire ties.
The lowest-ranked team left in the competition, National Conference Division One side Featherstone Lions, will be hoping to repeat a famous triumph of 21 years ago when they play host to League One Doncaster.
Hunslet will entertain their dual-registration partners Halifax while Batley Bulldogs and Dewsbury Rams welcome community clubs Lock Lane and West Hull respectively.
Sheffield Eagles, the 1998 winners, take on visitors Leigh Centurions, York City Knights travel to Barrow Raiders and Featherstone Rovers entertain Swinton Lions.
Conference outfit Siddal’s rearranged third-round tie at Workington Town will be staged this weekend with the winners hosting Newcastle Thunder.
Fourth-round draw: Keighley Cougars v Bradford Bulls, Whitehaven v Rochdale Hornets, Featherstone Lions v Doncaster, Barrow Raiders v York City Knights, Hunslet v Halifax, Featherstone Rovers v Swinton Lions, Sheffield Eagles v Leigh Centurions, Dewsbury Rams v West Hull, Workington Town/Siddal v Newcastle Thunder, Thatto Heath Crusaders v North Wales Crusaders, Batley Bulldogs v Lock Lane, Oldham v Widnes Vikings.
Ties to be played March 30-31
First-round draw: Hunslet v Workington Town, Oldham v Whitehaven, Doncaster v West Wales Raiders, Newcastle Thunder v Keighley Cougars.
Ties to be played May 3-5