Chester gave debuts to six players and welcomed back Simon Quinn after more than a year out with a knee injury.
The Gladiators got off to the perfect start when Dave Beddows opened the scoring in the opening minute. The referee penalised the visitors for leading with the forearm and Beddows, making his first start at hooker, burrowed over the close range.
Bradfield opened his account for the afternoon on 23 minutes to extend the Gladiators lead. The centre finishing off a neat team move that involved some quick hands from Dan Rowett and Damon Williams.
Rowett then added a try of his own, forcing his way over the whitewash from a few yards out and Quinn landed his first conversion of the afternoon to put Chester 14-0 in front.
The shell-shocked visitors recovered and a period of sustained pressure saw Chris Radford score Bury's opening try but the Gladiators hit back almost immediately. Bury spilt the ball 30 metres out and Chris Smith was quickest to react, racing 25 metres to score his first try for the club with Quinn's conversion giving the Gladiators a 20-4 lead at the break.
Chester moved further in front on 47 minutes when Bradfield bumped off three defenders to score a fine individual try but Quinn was off target with his conversion attempt.
Bury reduced the deficit with a try from Rick Brogan and their hopes of a comeback were given a boost on 61 minutes when Chester's prop Chris Young was sent to the sin bin for a professional foul. Bradfield wrapped up his hat-trick on 69 minutes to all but secure the win for the Gladiators.
Chester lost Andy Hill to the sin bin on 71 minutes for dissent but once again the Gladiators defence held firm. Fullback Quinn broke clear to grab a deserved try two minutes later despite Chester being a man short.
Playing the last 20 minutes with just 12 men meant Chester were out on their feet in the final few minutes and Bury scored a consolation try in the final minute through their man of the match Brogan.
Dan Rowett was named as the Gladiators man of the match, ahead of Bradfield and Quinn although Adam Whalin, who produced some fierce defence, and prop Michael Durham also impressed on their debuts.