In front of a capacity crowd, Finn Russell kicked 17 points from seven conversions and a penalty on his return from Six Nations duty with Scotland.
Saracens led 10-0 early on through Tobias Elliott's try and an Owen Farrell penalty.
But tries from Will Muir, Josh Bayliss, Alfie Barbeary, and Henry Arundell secured Bath the bonus point by half-time.
With Russell and England scrum-half Ben Spencer pulling the strings, they ran riot in the second period.
Spencer, Kepu Tuipulotu, Arundell, Guy Pepper and Bernard van der Linde ran in further tries to inflict a damaging defeat on Sarries.
Bath move three points ahead of Northampton at the top of the standings.
Saracens remain in sixth, four points adrift of the play-off places.