Ulster had a let-off after fourteen minutes, following a sustained period of pressure in the visitor’s 22 earned Bath a penalty, but Scottish out half Finn Russell couldn’t land kick.
The opening quarter remained scoreless despite both teams creating opportunities in attack only for accuracy to let them down at the crucial moment.
Bath finally broke the deadlock on 27 minutes, a 50:22 from Russell earned the home side an attacking line.
They executed a catch and drive move with the forwards probing at the line, before eventually Ulster infringed and conceded a penalty in the shadow of the posts.
Bath opted for a scrum, Alfie Barbeary controlled the ball at the base before feeding Ben Spencer. The scrum half threw a looping pass wide for winger Joe Cokanasiga to touch down in the corner. Spencer failed to convert.
Great defence from Rob Baloucoune three minutes later stopped a second Bath try, Spencer made a line break and hacked the ball on, but the Ulster winger won the foot race and touch down in goal.
Bath then won a penalty and Spencer made no mistake from in front of the posts.
Ulster hit back immediately, South African Rugby World Cup winner, Steven Kitshoff, won a turnover as Bath tried to run the restart out of their own 22, and the forwards probed at the line.
With a penalty advantage, Nathan Doak flung a pass wide, Bath centre Ollie Lawrence tried to hack it clear, but the ball came off Billy Burns knees and sat up kindly for the out half to gather and go over for Ulster’s first try with Doak adding the conversion.
Ulster turned the game on its head with a second try on 37 minutes.
Full back, Stewart Moore, fed Jacob Stockdale the ball, and the Irish winger set off on a counter-attack.
Stockdale fed James Hume and the centre exchanged passes in a confined space with Baloucoune.
Hume galloped clear before providing the scoring pass for Doak to run in under the posts.
Doak’s simple conversion gave Ulster a 14-8 at the interval.
HT: 8-14
Bath regained the lead five minutes after the restart with their second try.
Ulster conceded a penalty in their own 22, the home side went to the corner, Bath set up a driving maul from the lineout and hooker Tom Dunne with the help of a few backs was propelled over with Spencer landing the conversion.
Spencer added an easy three points from a penalty in front of the posts on 58 minutes after Ulster captain Iain Henderson infringed at the ruck.
Spencer missed the chance to extend Bath’s lead as he sent a penalty wide on 62 minutes.
Replacement flanker Matty Rea was yellow carded on 65 minutes on his own try line.
Bath made their numerical advantage count four minutes later, Ulster had conceded three scrum penalties under their own posts, from the third one Barbeary drove from the base, he was stopped short but replacement prop Thomas Du Toit barged over with Spencer converting.
Jake Flannery kicked the restart out on the full gifting Bath a scrum on halfway.
From the scrum, Russell came onto the ball at pace in midfield, he released Lawernce, the centre galloped into the 22 before popping the ball to Cokanasiga for the winger to go over for his second and Bath’s bonus point try.
Bath rounded off the victory with a fifth try in the final minute, replacement backrow Jaco Coetzee punched a hole in the Ulster defence the ball was quickly recycled and full back Matt Gallagher had an easy walk in with Orlando Bailey adding the conversion with the last kick of the game.
FT: 37-14
Scorers
Bath
Tries: Cokanasiga (x2), Dunn, Du Toit, Gallagher
Cons: Spencer (x2), Bailey
Pens: Spencer (x2)
Ulster
Tries: Burns, Doak
Cons: Doak (x2)
Line-ups
Bath
(15-9) Matt Gallagher, Joe Cokanasiga, Ollie Lawrence, Cameron Redpath, Will Muir, Finn Russell, Ben Spencer (C);
(1-8) Beno Obano, Tom Dunn, Will Stuart, Elliott Stooke, Charlie Ewels, Miles Reid, Sam Underhill, Alfie Barbeary.
Replacements: Niall Annett, Juan Schoeman, Thomas du Toit, GJ van Velze, Jaco Coetzee, Louis Schreuder, Orlando Bailey, Will Butt.
Ulster
(15-9) Stewart Moore, Rob Baloucoune, James Hume, Stuart McCloskey, Jacob Stockdale, Billy Burns, Nathan Doak;
(1-8) Steven Kitshoff, Tom Stewart, Tom O’Toole, Alan O’Connor, Iain Henderson (C), Dave Ewers, Nick Timoney, James McNabney.
Replacements: Rob Herring, Andrew Warwick, Marty Moore, Kieran Treadwell, Matty Rea, John Cooney, Jake Flannery, Mike Lowry.