Flanker Matt Garvey powered in for Bath's third try, converted by replacement fly-half Tom Heathcote, with their other 11 points coming from the boot of fly-half George Ford, who landed two penalties, a conversion and a drop-goal.
The visitors' powerful pack laid the foundation for the win as they outmuscled Wasps, forcing them to concede a succession of scrum penalties.
Right wing Jonah Holmes salvaged a late try for the hosts, who had won their previous two Aviva Premiership matches.
Bath went ahead in the third minute when their rolling maul led to a penalty, kicked by Ford.
Andy Goode missed two chances to open Wasps' account in the space of two minutes, first after Bath's former Wasps hooker Rob Webber tackled old team-mate Chris Bell off the ball and again when visiting full-back Nick Abendanon was offside challenging for a high kick.
Ford was well short with his second attempt, from just inside the Wasps half, after the home scrum collapsed.
The visitors doubled their lead when Ford atoned for his earlier miss with a superbly struck 40-metre drop-goal.
Bath elected to kick for touch rather than goal when the under-pressure Wasps scrum conceded another penalty, but the decision backfired when they infringed from the resulting lineout.
Wasps had to defend desperately after their pack handed Bath yet another penalty on the halfway line.
They conceded three more as the visitors strove to force their way through on the right, with the second resulting in a yellow card for Wasps prop Phil Swainston after he dragged down Bath's attacking maul.
Bath finally found a way through when former Ireland scrum-half Peter Stringer and Ford moved the ball left for centre Jonathan Joseph to send right wing Rokoduguni arcing in as he joined the attack on the left.
Wasps brought their big guns off the bench, introducing former England back-row man James Haskell for number eight Nathan Hughes at the start of the second half and current England lock Joe Launchbury for Kearnan Myall five minutes later.
But Goode missed a third penalty chance to open their account, pulling his long-range kick wide.
Another barnstorming Bath scrum had Wasps backpedalling frantically as they shipped yet another penalty, kicked by Ford to extend his side's lead to 14-0 after 58 minutes.
Two minutes later, Bath number eight Leroy Houston fended off former England lock Tom Palmer's poor attempt at a tackle to make the break and pass inside to send Rokoduguni on a clear run for his second try, converted by Ford.
Bath's inexplicable decision to go for goal with their next penalty, instead of chasing the bonus point, backfired when Ford missed.
When Wasps finally got quick ball from a scrum, replacement half-backs Charlie Davies and Joe Carlisle combined to send Holmes over in the right corner but Carlisle missed the conversion.
Garvey forced his way over for Bath's third try three minutes from time, with Heathcote converting, but they missed out on the winning bonus point their forward dominance should have delivered.
- Sports & Recreation
- George Ford