The flanker was among the try scorers as they overturned an early 10-0 deficit to power 19-10 in front by the break.
However, James Lowes’ side could then not build on that lead and they eventually fell away to lose for the first time in seven games.
It means – ahead of the last pool game versus Jersey at Scarborough on Saturday – their destiny is no longer in their own hands for quarter-final qualification; they must hope to garner enough points to finish as one of the three best group runners-up.
Still, Bainbridge was impressed by some of what they produced at a ground which has proved an unhappy hunting ground having already twice lost there in the Championship earlier this season against Scottish and Richmond.
“It was awesome to come down with the character we showed and the ability to actually play rugby,” he said.
“Some of the tries we scored were really good. But obviously it’s very disappointing to come away with a loss after playing some awesome phases of rugby.
“There was just a few errors that kept us out of the game.”
Carnegie – with fly-half Callum Irvine returning after almost four months out injured – were behind 10-0 inside just 12 minutes after Scottish captain Isaac Miller was driven over and Jake Sharp added the conversion and a penalty.
However, their response was fulsome with Mike Myerscough, Bainbridge and Andy Forsyth all running in tries before the break, Alex Davies adding two conversions.
From there, the visitors hoped to push on for the win but Scottish started the second period positively with Miller gaining his second try and Sharp improving again.
The game turned on the hour mark when the hosts regained the lead, scoring a controversial length-of-the-field try via Joe Smith when Carnegie had expected a penalty in their favour.
Sharp converted once more and replacement Nick Scott added their fourth try for some breathing space.
“We obviously travelled down on the day and started pretty slow; that affected us in the first 10 minutes when we had wanted to start really well,” added Bainbridge.
“But we changed it around, high-tempo rugby was our theme and we took that to them.
“Personally I think they couldn’t handle it and that’s why we scored 19 points unanswered. So, at half-time we were sitting pretty well but there was quite a lot of pressure on us to come out that second half and start how we’d ended the first.
“We didn’t manage that but we’ve come a long way since losing 30-3 to Jersey in our first B&I game and now we’ll look to take it to them on Saturday.”