Bristol ran in five tries as they claimed their ninth consecutive league win, with victory at Coventry.
Lee Robinson, Ross Johnston and Redford Pennycook all touched down in the first half as Bristol led 17-6 at half-time.
A second try for Johnston and a late effort from Junior Fatialofa completed the scoring for Paul Hull's side.
A second-half penalty from Coventry's Fangatapu Apikotoa, his third overall, and a last-minute try from David Askew reduced Bristol's victory to 11 points.
Bristol head coach Paul Hull told BBC Radio Bristol:
"The first half was very good. We dominated field position and got three tries.
"In the second half, I'm not saying we took our foot off the gas, but we didn't quite dominate in certain areas of the game.
"I'm pleased to see the guys aren't jumping for joy even though we got a bonus-point victory as that shows they really want to improve."
Bristol: L Arscott; L Robinson, J Adams, J Fatialofa, T Arscott, A Jarvis, J Spice; M Irish, R Johnston, D Crompton, N Budgett, R Winters, J Phillips, R Pennycook, I Grieve. Replacements: D Blaney, W Thompson, B Glynn, D Montagu, R Shaw, S Giddens, D Norton
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