Bath were awarded a penalty try in the first half and followed up with further touchdowns from Tom Biggs and Kyle Eastmond. Fly-half Tom Heathcote kicked four penalties and two conversions. Henry Trinder and Jonny May (2) scored the Gloucester tries with Freddie Burns converting one and Rob Cook adding two penalties and two conversions.
Booth said: "It wasn't just because we know how important it is, playing Gloucester. I read that they've won the last five times that they've been here so it was important to break that cycle."
He continued: "In the context of the season, we knew that the end of February and March were going to be very important. We had a good opportunity to bridge the gap at Northampton last week and didn't. We had to bounce back. That resilience I think is more evident each week. We want to fight tooth and nail for everything we can get."
Bath have slipped into a free-scoring style in recent weeks, a marked change from the safety-first tactics they employed in the early part of the season.
Booth added: "Everyone can hopefully start to see that since the turn of the year we've adopted a more ball-in-hand approach. That's the one thing in rugby - it doesn't matter how well organised they are, if you've got pace and quick ball you are going to create problems for people.
"Three times when we did it, we showed the skill and execution to get past them. That proved to be the difference."
Gloucester director of rugby Nigel Davies confessed his doubts about the dismissal of hooker Darren Dawidiuk, saying: "I'd like to see it again but I don't really think it was a red card."
But he was more than satisfied with the way his team reacted to that setback. He said: "I was delighted with that last period, the last 30 we played with 14 men. For the boys to respond like they did was fabulous. That's the character that this team has shown this year.
"That's important. There's a lot of technicality in the game and parts of that we got badly wrong. Our set-piece was poor. It didn't allow us to control the game for long enough periods. But as long as you've got character in the team, you've got a chance."