The home team's punishing driving maul laid the platform for three of their tries, including first-half touchdowns by flanker Alafoti Fa'osilva and scrum-half Micky Young.
Gavin Henson came off the bench against one of his former clubs to claim the third early in the second half but it was just five minutes before the end that Guy Mercer claimed the bonus point try for the runaway Pool 3 leaders.
Owen Williams was making his first appearance for Cardiff since pulling a hamstring playing for Wales against Australia on 30 November. The only other first-team regular was his centre partner, Chris Czekaj as the Blues recalled a host of younger players from Principality Premiership clubs.
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Bath, led by Welshman Dominic Day, were also much-changed but armed with plenty of first-team experience.
Cardiff opened the scoring after six minutes with a penalty by fly-half Simon Humberstone but it took Bath barely two minutes to respond, Ryan Caldwell's line-out take setting up the drive for an unconverted try by Fa'osilva.
The Samoan then showed his defensive capabilities with a try-saving tackle on Owen Williams.
A strengthening wind helped Cardiff maintain a territorial advantage but also spoiled Humberstone's attempt to add a second penalty on 22 minutes.
Instead Bath broke clear, forced a penalty to the corner and another catch-and-drive yielded a 27th-minute try for Young under the posts. Tom Heathcote added the conversion.
Fa'osilva showed his sevens pedigree with a 50-metre burst from the restart but the Blues scrambled back and might have scored a try themselves only for Owen Williams to waste a three-to-one overlap.
But they had been awarded a penalty in front of the posts and Humberstone made the half-time score 12-6 as a squall drenched the Rec, again near capacity at just under 12,000.
Bath were 19-6 ahead 10 minutes into the second half as former Wales star Henson came off the bench - and scored his first try for Bath almost straight away. Heathcote added the conversion.
A thrilling break by Owen Jenkins down the right, supported by skipper Ellis Jenkins, for once had the Bath defence stretched to breaking point. But, after some inventive interpassing left and right under the Bath posts, Tom Biggs rushed up to close down the space and the chance was gone.
Bath had struggled to establish field position but that was remedied when Heathcote kicked to the corner from a penalty and the driving maul did the rest.
Mercer emerged with the ball but Heathcote's conversion attempt struck the post.
Cardiff hit back with a well-worked try for full-back Dan Fish, converted from the touchline by Humberstone.
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