With two shots came two goals within 18 minutes of the game, with both going the way of Bedricks, making their higher Division experience count.
It was 0-1 to Bedricks after just 2 minutes, as a right wing corner was met by a towering header from Joe Allen into the roof of the net.
Arguably, Bury - who are the official Bury Town FC Sunday side and playing at the main club's ground for the first time - played the better football and really had the more of the major chances, but Bedricks were soon two goals ahead as a ball squared across to Brandon Salisbury saw the latter stick out a foot and turn it home from point blank range.
Bedricks however did have a great chance on 21 minutes, after hooking a great ball over the onrushing Dan Stobbart, Harvey Hubbard though was around to clear the danger.
Bisons meanwhile went agonisingly close three minutes later, a left wing corner fell to Ed Spampanato whose audacious first time volley on the edge of the box rebounded just wide off the outside base of the right hand post.
Up the other end though, Bedricks had another good chance, Brett Codd's shot from inside the box though was deflected wide into the bottom near side-netting. And from the resulting corner, goalscorer Salisbury peeled away cleverly at the near post, but glanced his header just wide of the top far, right-hand, corner.
Bisons meanwhile continued to look for a goal back, as Owen Walton-Ross' fierce 35-yard low strike was deflected narrowly wide for a corner.
But it was Bedricks who had the final chance of the half - a right wing corner found Salisbury leaping highest, only to glance his header just wide of the top far corner.
Ten minutes after the restart a fantastic double stop from Bisons goalkeeper Dan Stobbart thwarted a third Bedricks goal. Suckley broke through dangerously down the right wing, the Bedricks man then sqaured a great ball across the box, where the shot from point blank range was clawed away brilliantly by Stobbart, who was still on the ground when he denied the follow up shot.
At the other end, his opposite number James Griffin made a tremendous save to deny Owen Walton-Ross, flying across to his top left hand corner to beat away the fierce strike, keeping it at 0-2 after 61 minutes.
From the resulting corner, Bisons deservedly broke through, the set-piece found Will Stobbart in space, who brilliantly sidefooted his low strike into the bottom left hand corner, despite Griffin getting a hand to it, 1-2 with 28inutes remaining.
Another superb stop from Griffin however prevented Bisons from drawing back on level terms on 72 minutes, a fantastic Bisons strike was arrowing into the top right hand corner until the Bedricks stopper dived across to tip it behind.
Since the goal, Bisons were dominating more of the possession, and had another good chance on 86 minutes as Jordan Asker swerved a clever long range dipping strike, albeit it was straight at Griffin.
Bedricks though took back control, looking to see out the remaining ten minutes, with Salisbury's header from a corner, which looked destined to nestle into the top left hand corner, being headed off the line by the well placed Will Stobbart. The rebound strike meanwhile was easily saved by Dan Stobbart.
An outrageous stop from the latter kept Bisons in with a chance of grabbing an equaliser in the 87th minute, goalscorer Allen looked to dip a great volley past Stobbart, who was slightly off his line, only for the stopper to produce a superb stop to tip it over onto the roof of the net.
Bedricks meanwhile had another great chance four minutes into added time, after Allen cut through neatly onto the byline, his cutback found Macauley Delo, whose shot was deflected behind for a corner.
Two minutes later, some determined Bury defending ensured that Bedricks wouldn't add a third goal, first a Bedricks substitute saw his shot well saved by Stobbart, who then smothered Charlie French's follow up effort well off his line, from close range, allowing Bury to clear the danger.
However, that was that as Bedricks triumph in a cup competition for the first time in their history, following 2 first half goals.
Bury Town Bisons:-
1 Dan Stobbart
2 Ed Spampanato
16 Joe Hogg
77 Harvey Hubbard
3 Dan Williams
7 Jordi Asker (c)
22 Will Stobbart
10 Harry Bentley
15 Owen Walton-Ross
9 Liam Mills
20 Luke Bates
Subs:
29 Callum Chambers-Shaw
5 Joseph Gilbert
Bedricks Worth:-
1 James Griffin
2 Connor Suckley
3 Jonathan Moye
4 Callum Smith
8 Charlie French
9 Brett Codd
10 Elliott Chaplin
11 Macauley Delo
14 Kerrin Lawrence
16 Joe Allen
7 Brandon Salisbury
Subs:
Liam Grant
Callum Paxton
Ronnie Ward
Booked: Mills (32'), Bed6 (90'+2')
Sin Binned: Walton-Ross (90'+5')
Goals: W.Stobbart (62'); Allen (2'), Salisbury (18').