Bristol (10) 37
Tries: Robinson, Adams, Irish, Arscott, Giddens Cons: Jarvis 3 Pens: Jarvis 2
Bedford (16) 16
Try: Dodge Cons: Pritchard Pens: Pritchard 3
Bristol ran in five tries in two hugely contrasting halves on Friday night to eventually run out convincing winners at the Memorial Stadium.
Paul Hull's side gifted Bedford Blues most of their points as three penalties and an Ollie Dodge try gave the visitors a 16-10 half-time lead.
But Bristol, who had been in front from an early, converted Lee Robinson try, flew out of the blocks after the break.
Tries from Jack Adams, Mark Irish, Tom Arscott and Sam Giddens sealed victory.
After trailing at the break, it took nine minutes of the second half for Bristol to hit back.
Centre Adams powered through, Adrian Jarvis converted to take them back in front. And Jarvis then landed his fourth kick of the night with a second penalty two minutes later to earn a 20-16 lead.
It was then tight for the next quarter of an hour until prop Irish scored try number three to carve a nine-point lead and effectively seal victory.
And two more tries in the final eight minutes from full-back Tom Arscott and and Kiwi utility back Sam Giddens, who had only just come off the bench, rounded off a much-improved second-half display.
This latest victory for second-placed Bristol was their fourth bonus-point victory in five matches.
And, after moving to within a point of top spot, it sets them up nicely for the first versus second clash at leaders Exeter on 27 December.
The Chiefs suffered their first defeat of the season on Saturday, a 23-13 local derby defeat at Plymouth Albion.
Bristol: Arscott; Robinson, Adams, Fatialofa, Norton; Jarvis, Spice; Irish, Blaney, Thompson, Budgett, Winters, Grieve, Pennycook, Montagu
Replacements: Bellamy (80), Crompton (71), Miller (74), Giddens (74) , Eves (74)
Not used: Sambucetti, Shaw
Bedford: Pritchard; Fielden, Dodge, Roberts, Davey; Dorrian, Walshe; Walsh, Richmond, Boulton, Howard, Harlock, Gillanders, Goodman, Tupai
Replacements: Locke (70), Seal (70), Rae (62), Harding (62), Vass (70), Davies (58), Knight (52)