Louis White bagged a try in either half while Jacob Mitchell, Jamie Howick and captain Joe Wooler all touched down for the Cubs, with four conversions from Fin Fielder and one from Eamonn Rogers completing the scoring in Cornwall.
Max Ferguson grabbed a consolation score for the Chiefs, but the Cubs now wait to see where they will finish in the Southern Pool and who they will face on Finals Day.
Bristol Bears: 15. Jake Smith (Collegiate & Chew Valley RFC), 14. Louis Nancekivell (Bristol Grammar School), 13. Jamie Howick (Wellington School), 12. Jacob Mitchell (Clifton College), 11. Aidan Boshoff (Clifton College), 10. Fin Fielder (Clifton College & Chippenham RFC), 9. Ted Phillips (Clifton College); 1. Louie Trevett (Clifton College & St Albans RFC), 2. Oscar Simms-Preston (SGS College), 3. Louis White (Collegiate & Chew Valley RFC), 4. Ollie Thraves (QEH & St Brendan’s RFC), 5. Joachim Hullah (SGS College & Hornets RFC), 6. Joe Wooler (Clifton College & Chew Valley RFC), 7. Sonny Davis (SGS College & Hornets RFC), 8. Tom Gardner (Clifton College & Tondu RFC).
Replacements: 16. Arthur Davis (SGS College & Cleve RFC), 17. George Payne (Clifton College & Clifton RFC), 18. Kenzie Jenkins (Coleg y Cymoedd & Mountain Ash RFC), 19. Archie Prewett (SGS College), 20. Joe Webb (Hartpury College & Pentyrch), 21. Will Knight (Prior Park College & Chew Valley), 22. Eamonn Rogers (Clifton College).