Bath started strongly and it took some determined defence by Wasps to hold them out.
The men in black and gold hoops also had chances to open the scoring in the first five minutes of the game but Bath’s defence was strong.
The hosts then launched an irrepressible attack on eight minutes. Bath first lost the ball over the line thanks to some massive hits from James Downey and Ehize Ehizode, but the referee brought play back for a penalty.
From the resulting phases Bath hooker Dan Frost piled over the line to score off the back of a maul. Fly half Laurence May added the conversion to make it 7-0.
The home side were dominating possession and territory and soon after they set winger Jeff Williams free down the touchline. Alex Lozowski came across at speed with a great cover tackle to bring the former England Sevens player down.
In the 12th minute Bath extended their lead with a second try. Centre Max Clark smashed his way over from close range. May just missed the conversion to leave it at 12-0.
United continued to push for more points but some enormous tackles from Wasps in defence managed to keep the home side at bay.
After 20 minutes it was Wasps’ turn to get on the board. The visitors turned the ball over on halfway and charged into the Bath half through some great carries by Guy Thompson and Tom West. Wasps were then awarded a penalty and they opted for the posts. Lozowski slotted it over to make it 12-3.
Both sides had their chances to get the next score before half time with Wasps forced to rely on a fine try saving tackle by Tom Stileman and Bath only just managing to scrag Owain James as he tried to escape down the wing.
Five minutes before half time Guy Thompson was shown a yellow card for a late hit and the momentum once again swung in the home sides favour.
On the stroke of halftime Bath won a penalty at the scrum and May pointed at the sticks. The fly half made no mistake with his kick to make it 15-3 as the two teams headed into the sheds for halftime.
Wasps made two replacements at half time with Jake Charters and Will Wilson coming on for Will Stuart and Alex Rieder.
However the changes did not alter the flow of the game as Bath went back on the attack almost immediately. Another try from a maul eventually came and number eight Aaron Carpenter was the beneficiary. May missed the conversion to leave the score at 20-3.
Alex Lundberg then joined the action and made an immediate impact as Wasps hit back. The loosehead prop and Sailosi Tagicakibau put in some nice build up play to allow Ben Jacobs to stroll over in the corner. Lozowski converted to make it 20-10.
Wasps were showing signs of a somewhat unlikely comeback and were enjoying much more possession since the break.
Although Bath remained a threat throughout and it took a monstrous hit from Lozowski and a crucial turnover from Will Wilson to stop a creaking Wasps defence from breaking.
Then with six minutes to go it looked as though Wasps had fashioned themselves the opportunity they were after, but the visitors knocked it on right on the Bath line and Wasps’ hopes of a win appeared to vanish.
But four minutes later an unlikely win was back on as full back James charged down a kick and followed it up to dot it down for a try. Lozowski converted to make it 20-17 with two minutes left.
The win wasn’t to be forthcoming for Wasps though as the last passage of play belonged to Bath. The home side tried everything they could to take the losing bonus point away from Wasps with the final act of the game. In the end Bath were satisfied with the win, so they kicked it out of play to end the game.
After the game A League coach Matt Davies said: "After a disappointing first half where we weren't quite at the races with our execution and our energy, we were really pleased with the second half to take it back to 20-17. After which we had a number of opportunities to even win the game.
"It was a great experience for some of the younger players to play alongside older guys. Hopefully we'll take the lessons from the game and move onto Exeter in two weeks time."
Wasps return to A League action in two weeks time when they take on Exeter Braves at Sandy Park on 11 April.
Tries: Dan Frost,Max Clark, Aaron Carpenter
Conversions: Laurence May 1/3
Penalties: Laurence May 1/1
Tries: Ben Jacobs, Owain James.
Conversions: Alex Lozowski 2/2
Penalties: Alex Lozowski 1/1