The bulk of their total of 326-7 was supplied by Jordan Smith and Thomas Hankins, who put on 211 for the second wicket.
Hankins was first to go for a rapid 123 from 97 balls before being run out, with Smith following for a more patient 128.
Despite an early victim for Jordan Price (1-25), Bedminster steadily ate into the Lansdown total before the wickets began to fall at regular intervals.
Skipper Hankins was the key man as he removed Garreth Elphick for 41 and Mark Alleyne for 33 among figures of 3-42.
Reece Croker, Chris Day and Sam Bowery also removed two Bedminster batsmen as they were dismissed for 166.
Lansdown are tied for third with Keynsham.