However, a stunning comeback - inspired by two tries from fly half hero Andy Goode - saw Warriors claim maximum points and open up a commanding 12-point lead over Bedford Blues, who lost at Cornish Pirates, at the top of the RFU Championship.
"We made a big stride forward," said Hill. "The atmosphere, with the numbers in the crowd and a team that had played in the Premiership, was the kind of test we will encounter in the play-offs.
"The test was could we cope with the pressure, because we were the favourites, and come here in front of packed house and get a good win and a good performance - we have done both those things.
"The key is can we cope with the pressure come the play-offs and hopefully semi-finals? Can we come back from 15 points behind and have we got the bottle to have the belief to comeback. This result was a massive step forward. I was always confident this group of players had the confidence to comeback.
"Bedford losing as well is a good for us and has opened up a gap. Our aim is to have top place secured by the time we play Birmingham. Then we can rest some players and prepare for the play-offs. We want to go another win clear and have Bedford at home next week so we can push further ahead."
Hill admitted he was not surprised by a flying start from the hosts as they stormed into a big lead.
However, Warriors drew level before the break before taking complete control after the interval to cruise to another league victory.
"We fully expected Bristol to start well - every game they play they go off like a train," added Hill. "They play off adrenaline for the first 20 minutes and won all the collisions. Our defence was struggling to cope with their intensity.
"But you can only live off adrenaline for 20 or 30 minutes; then you have to rely on your core skills. We had to take 20 minutes of adrenaline off Bristol and were 20-7 down which was disappointing and mildly worrying.
"Towards the end of the first half we started to turn then screw and get control. The pleasing thing for me was that we didn't go into our shell, we saw a fantastic counter-attack just before the end of the half and we had the confidence to run from deep. We also had a try disallowed after more great play.
"The signs for me at the end of the first half were that we had the confidence to come back. At half-time I was a lot more confident at 20-20 that our superior fitness and our strong bench would tell and it did."