The visitors top Pool 1 of the competition and the result of the Newport-Gwent Dragons game against Saracens, which fell victim to the weather on Friday night, is now irrelevant.
Second row James Hanks, who only returned to first-team duty during last weekend's win at Wasps following a knee injury, led the Chiefs as loosehead prop Ben Moon returned to the fold after injury.
There were also first starts of the season for tighthead prop Chris Budgen, Samoan international scrum-half Junior Poluleuligaga and academy youngster Jack Arnott on the left wing.
Bath included hooker Lee Mears for his first start since returning from injury, lock Dave Attwood and centre Matt Banahan in their starting line-up after they were released earlier in the week from the England squad.
The visitors took the lead after seven minutes as Biggs chased a chip through from full-back Sam Vesty, but he looked to have been tackled off the ball by centre Bryan Rennie.
Welsh referee Neil Hennessey referred the decision to television match official Tony Spreadbury and, after a long deliberation, the try was awarded with centre Olly Barkley adding the extras.
Spreadbury was called into action five minutes later as centre Sam Hill charged down a kick from Bath fly-half Stephen Donald before hacking on, but it was adjudged that wing Olly Woodburn beat him to the touchdown.
Bath increased their lead when Donald chipped through for Biggs to touch down for his second try, but Barkley was off target with the conversion and the Chiefs hit back through a Myles Dorrian penalty.
Biggs completed his hat-trick on the half hour as he intercepted a pass by Dorrian and ran in from 60 metres. Barkley added the extras for a 19-3 interval lead.
After some scrappy play from both sides at the start of the second half, Chiefs were awarded a penalty 10 metres out in front of the posts.
They opted for a scrum, but Bath were able to clear their lines.
Bath used the same option a couple of minutes later when they were pressing the Chiefs line after hooker Chris Whitehead had been sent to the sin-bin, but the home side were also able to clear.
After an injury to Chris Cook, the visitors gave a debut to Welsh international scrum-half Warren Fury, who recently agreed a three-month deal with the club.
The visitors secured maximum points from their four pool games as their bonus-point try came on the hour when flanker Guy Mercer gave the final pass to right wing Olly Woodburn to touchdown.
The Chiefs were forced to play the final six minutes with 14 men when Rennie was carded.
And replacement flanker Josh Ovens made the extra man count when he crashed over for Bath's fifth try, Barkley adding the extras to complete the scoring.
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