The former England striker was substituted immediately after heading in his 304th goal for Wolves 11 minutes from time, to join former Molineux playing icon John Richards on 18 League Cup goals.
Bull, 33, has undoubtedly been invigorated by playing alongside the buzz- name of the Nationwide, Robbie Keane, who also scored twice as Wolves cantered through to the second round of the Worthington Cup. Having lost the first leg 2-1, they qualified 6-2 on aggregate.
Wolves went straight for the throat from the off and in the sixth minute Keane combined with Kevin Muscat on the right.
Bull did not have long to wait. Receiving left-back Lee Naylor's throw inside his own half, Bull sent a raking pass out wide to the other flank. Keane bided his time before swerving back the ideal cross for Bull to run onto, stoop and head into the corner. It was one of the longer one- twos of the season.
If Mark McGhee's team are to follow up their good early-season start in the First Division, and make a convincing shunt for promotion, they will be eager to add composure to last season's midfield. In Fern-ando Gomez, making his home debut last night, they may have found the necessary addition.
Nine minutes from the interval the former Spanish inter-national midfielder pulled the ball back onto his left foot and delivered a centre so precise it must have landed on the Wolf head of Bull's shirt. The rest was a formality.
Keane added to the rout almost on half-time. And he scored the cutest goal of the night when, 16 minutes from time, he ran on to Bull's header to chip the goalkeeper almost from the byline.
Bull's treble was completed five minutes later when he ran in gleefully unmarked to head in a Steve Froggatt corner which he himself had earned. Par for the course, really.
Wolverhampton Wanderers (5-3-2): Stowell; Muscat, Curle, Sedgeley, Richards, Naylor (Gilkes 80); Gomez, Osborn, Froggatt; Bull (Jones 80), Keane. Substitutes not used: Atkins, Bray (gk), Williams
Barnet (5-3-2): Harrison; Stockley, Goodhind, Bashan, Ford, Currie (Harle 80); Simpson (Manuel 71), Doolan, Onwere; Devine, McGleish (Charlery 73). Subs-titutes not used: Rust (gk), Wilson.
Referee: S Baines (Chesterfield).