George Ford pulled the strings for the hosts from scrum-half and was responsible for 20 of their points as they recorded their biggest ever win over Leicester.
Five different try scorers crossed the line for Bath as they moved top of the table with a third consecutive win at the start of the season, the first time they have done so since 2003-04.
For Leicester, it was disappointing day as their winning start to the campaign came to a shuddering halt and to make matters worse it was the first time in 10 years they have been held scoreless.
Saracens are the only other side to record three wins at this early stage of the season as they came from behind to record a 36-32 win over London Irish.
Owen Farrell and Andy Goode kicked well for the visitors at the Madejski Stadium, while Tim Streather, Richard Wigglesworth and Billy Vunipola socred their three tries.
Defeat meant Irish winger Alex Lewington's hat-trick of tries were in vain as they were unable to record back-to-back wins.
Northampton Saints kept pace with the top two thanks to a 35-10 victory at Newcastle Falcons on Sunday, with the visitors running in four tries.
A 25-point lead at half-time gave the Saints complete control of the game and although the second half was much closer Newcastle were unable to come back and record their first win of the season.
Meanwhile, at Kingsholm, Exeter Chiefs edged a tight encounter with Gloucester to win 25-22.
Exeter, inspired by Gareth Steenson's 14 points, were impressive in the first half as they amassed 22 points before clinging onto their victory despite a Gloucester fight back.
Another close game saw Harlequins turn a first-half deficit around to beat Wasps 26-23.
Having only scored nine points before the break Harlequins added another 17 in the first 20 minutes of the second half to secure the win.
Elsewhere, Sale Sharks picked up their first victory of the new season as they condemned bottom-of-the-table London Welsh to a 46-8 defeat.