With the top three of Leeds, Wigan and Wakefield, getting plenty of attention, Warrington are travelling under the radar but that suits Burgess, with England captain George Williams set to make his comeback in one of the next two games and a home play-off within reach.
Williams’ return will boost Wire but 18-year-old Irwin and Leon Hayes, 22, proved an effective half back pairing, with the kicking both out of hand and off the tee superb.
Ethan Ryan had begun the scoring for the hosts with his 13th try of the Super League season on 14 minutes, Luke Hooley missing the extras – but that was as good as it got for the Bulls.
Ashton benefitted from slick hands by Josh Thewlis, Hopoate carried ball and Ryan over for a second before King and Irwin’s boot sent Wire in 18-4 to the good at half time.
Things might have been different had the home side’s Jamie Gill not had a try ruled out after Chris Atkin pulled back recovering defender Danny Walker, but within 60 seconds Wire were up at the other end with Philbin going over for a fourth.
It was a potential 12 points swing which sucked belief from the Bulls and from there, Warrington put their foot down.
Crowther scored six minutes later, Bradford dazzled by some dizzying angles, and Irwin’s twinkling feet added another before Ashton rounded things off with his second of the night.
Bradford: Aekins, Wynne, Holley, Fulton, Ryan, Dean, Atkin, Dean; Gardiner, Ackers, Gill, Sutton, Peposhi, Mellor.
Interchanges: Doyle, Scurr, Lewis, Leake
Warrington: Thewlis, Webster, Hopoate, King, Ashton, Irwin, Hayes, Byrne; Walker, Harrison, Holroyd, Bentley, Currie.
Interchanges: Sipley, Crowther, Philbin, Tanginda.
Referee: Aaron Moore.