Webb was made available to gain match fitness following his recovery from an ankle injury.
He was replaced at the break by Matthew Aubrey and will rejoin Wales' preparations to face Italy in their Six Nations start in Rome on 5 February.
Ospreys rose to second in Pool Two, on 10 points apiece with leaders Exeter.
But the focus of Wales fans was on Webb who again expressed confidence in his conditioning with the Six Nations in mind before rejoining the Wales squad on Monday
"I'm not just going in there to make up the numbers," said Webb.
"I'll be going in there to fight for that jersey back. I feel fit, ready and raring to go."
The 28-year-old, who has 23 Wales caps, scored on his 60-minute return from an ankle injury in the 26-21 European Challenge Cup win at Newcastle last weekend.
"I'm 100% fit. I feel good. I didn't  want to come off last week, but was just sticking to the guidelines with the physios and conditioning coaches and same again in this game," added Webb.
"They know best, they know my body.
"I don't want to come off after 60. I don't want to come off after 40.
"I feel I can go on for a lot longer. I've had a good block of rehab and fitness training to get me back where I need to be and I'm loving it at the moment."
Against Bristol, full-back Dafydd Howells went over for a try converted by Luke Price and Max Crumpton hit back for the visitors before the break.
Replacement Welsh hooker Marc Jones' try put Bristol ahead going into the latter stages, but Bath-bound open-side Sam Underhill's late score and Price's conversion ensured Ospreys' win.
Ospreys: Dafydd Howells, Jay Baker, Joe Thomas, Jonathan Spratt, Ben John, Luke Price, Rhys Webb (capt); Gareth Thomas, Scott Otten, Rhodri Jones, James Ratti, Adam Beard, Joe Bearman, Sam Underhill, Rob McCusker.
Replacements: Ifan Phillips, Rowan Jenkins, Daniel Suter, Tyler Ardron, Will Jones, Matthew Aubrey, Phil Jones, Tom O'Flaherty.
Bristol: Jack Wallace; David Lemi, Will Hurrell, Tusi Pisi, Tom Varndell; Billy Searle, Alby Mathewson; Jack O'Connell, Max Crumpton, Gaston Cortes, Dan Tuohy, Ben Glynn, Nick Fenton-Wells, Jack Lam (capt), Mitch Eadie.
Replacements: Marc Jones, Jamal Ford-Robinson, James Hall, Mark Sorenson, Giorgi Nemsadze, Rhodri Williams, Thretton Palamo, Jack Tovey.
Wales scrum-half Rhys Webb came through his pre-Six Nations run-out for Ospreys in their 20-14 Anglo-Welsh Cup win over Bristol.