Fly-half James Grayson opened the scoring and proceeded to pull the strings until he was withdrawn 20 minutes from time.
Francois van Wyk added two further first-half tries to Grayson's earlier effort, and Saints scored four more after the break.
Alex Mitchell, Reece Marshall, George Furbank and Andrew Kellaway were all on the mark as the black, green and gold totally overwhelmed their visitors on a crisp afternoon at Franklin's Gardens.
It was all Saints early on and after the forwards took them within range, the ball was moved to the left for Grayson to dive over in the corner.
The fly-half just missed the tricky touchline conversion and he did so again soon after as Saints scored again, through van Wyk.
The prop picked up his first Saints try thanks to a second charge-down in the space of a few seconds from the home side as Bristol continued to play with fire in their own 22.
But the Bears finally bared their teeth on 22 minutes as they kicked a couple of penalties to the corner and ramped up the pressure, rumbling over thanks to hooker Tom Lindsay.
Saints immediately won a penalty after the restart, allowing Grayson to add three more points to their tally.
And the No.10 was at it again soon after, taking the score to 16-5 as his side continued to take points from every venture into Bears territory.
That pattern continued as Saints put the pressure on from a five-metre scrum and Mitch Eadie's quick tap penalty opened the door for van Wyk to score his second.
Grayson quickly converted and Saints were in total scoreboard control.
The black, green and gold almost grabbed a picture-book try before the break as a move started by a lovely Luther Burrell offload ended in Grayson spilling the ball over the line under pressure.
But Saints did get their bonus point before half-time as some lovely combination play between Grayson and Burrell allowed Mitchell to score.
Grayson converted well to put the icing on the first-half cake and Saints picked up where they left off at the start of the second period, scoring a fifth thanks to returning hooker Marshall.
Grayson added the extras once again and Bristol looked desperate to get back on the bus with a full 30 minutes remaining.
But they did have something to shout about when Jordan Crane was driven over after Saints had done well to scramble to stop Tom Pincus from scoring.
Madigan converted, but Saints went straight back up the other end to score, with full-back Furbank finishing the move.
Grayson converted and there was still plenty time for more celebrations, with two replacements combining as Mike Haywood offloaded well for Kellaway to score.
Furbank kicked the conversion well from out wide, but Bristol quickly responded as Madigan's tidy crossfield kick found Pincus, who finished well.
Madigan missed the conversion, but his team were now on the hunt for a try bonus point with seven minutes remaining.
And they were to get it thanks to Jack Lam's last-gasp score, with Madigan converting.
Saints: Furbank; Sleightholme, Dingwall, Burrell (Strachan 64), Worley; Grayson (Kellaway 60), Mitchell (Davies 52); van Wyk (Davis 52), Marshall (Haywood 64), Garside (Higgins 70); Moon, Barrow (Craig 60 (Barrow 74)); Wood (c), Ludlam (Onojaife 64), Eadie.
Bristol Bears: Pincus; Powell, Bedlow, Pisi (cc), Perkins (Lloyd 55); Madigan, Stirzaker (Cullen 74); Lay (Cosgrove 68), Lindsay (Capon 74), Thomas (Armstrong 47), Ehizode, Batley, Lam, Heenan, Crane (cc).
Referee: Shaun Harding