Mark McCammon, who is hunting down a contract with City, made a great start to his home debut with a goal after seven minutes.
It should have put the side he has joined on loan from Brighton well in control. Indeed it did but they failed to take their chances and once James Hayter had levelled in time added to the first half, Bristol had a hard fight on their hands although the final score line was comfortable enough.
McCammon's strike, right-footed from 14 yards, was set up by teenager Steve Cotterill, who took the ball off Bournemouth skipper Neil Young on the edge of the box.
It was not a good half for Young who picked up a card for tripping over Cotterill some 30 yards out and in front of goal.
Once again City, after dominating the play, failed to take advantage allowing defenders to scramble the ball away.
Gareth Stewart then made good saves from Stephen Brooker and McCammon to keep Bournemouth in the game aided by an expensive miss by Scott Murray.
Again the build up was between Cotterill and the new signing but Murray's first touch let him down as he missed the target from 10 yards.
That miss looked doubly expensive when Hayter's looping effort found the top left hand corner for his 17th goal this season.
It was down to a defensive mix up by Bristol for when Louis Carey lost out in the air, there was no cover as Hayter, a transfer target recently for City, raced clear.
A strong cross-shot from Fletcher was not far from seeing Bournemouth going in front early in the second half but Young's jinxed afternoon had one further twist.
An outstretched heel made a significant deflection as Brooker restored Bristol's lead 11 minutes into the half but as the shot was on target Young escaped an own goal but Bristol's resolve was now high and Brooker sealed their win with a well drilled shot from the left channel.