Three months after losing 25-21 to Saints in last season's final at Twickenham, Johann van Graan's side ran in five tries in a bonus-point victory.
Joe Cokanasiga, Ted Hill, Ben Spencer, Ollie Lawrence and replacement Jaco Coetzee scored for the home side, while Finn Russell kicked five conversions and a penalty.
Flanker Josh Kemeny touched down on his Premiership debut for Saints, while Fin Smith booted a conversion and three penalties but they outgunned on the night by a Bath side seeking revenge.
Bristol also got off to a winning start on Friday with a 24-3 victory away at Newcastle.
The home side put up a tougher fight than when they suffered a record 85-14 defeat at Ashton Gate five months ago but still fell to their 22nd league defeat on the bounce.
A brace from Max Malins and tries from James Williams and Siva Naulago, with AJ MacGinty adding two conversions, delivered Bristol's bonus point win at Kingston Park.
