Opening batsman Henry Thompson (97 not out) fell just short of his century, carrying his bat as the Roosters posted 189/8 from their 50 overs.
Sanjay Mani, Matthew Stewart and Craig Broadley then took two scalps apiece as Bridge were knocked over on 118.
Saturday’s victory was Harrogate’s 10th in 17 completed league fixtures this term.
Already safe from relegation, ninth-placed Sessay suffered a final-day defeat when they entertained a Scarborough side who needed to win to guarantee their own survival.
Chasing the Seasiders’ total of 222/5, the Thirsk outfit were bowled out for 166, Matthew Till making 37.
Studley Royal head into their final fixture fourth in Yorkshire Premier League North Championship West and still in with a chance of promotion.
They beat second-placed Whitkirk by 64 runs and now sit just seven points behind them in the table.
Dan Craven top-scored with 76 in the visitors’ 211 all out before three wickets apiece for Michael Litterbach, Craven and Leo Wilson helped get rid of the home team for 147.
Fifth-placed Harrogate 2nds posted 234/9 at home to Thirsk, Ollie Horberry leading the way with a knock of 67 as James Wilkinson claimed 4-39.
Josh Crewe contributed a defiant 77 when the away side replied, however 5-22 from William Harwood ensured that their response did not progress any further than 138.
Greg Pickles (45) and Henry Perham (41) were among the runs for Knaresborough as they made 205/9 on their way to a two-wicket defeat at York 2nds.
Bilton-in-Ainsty continue to hold onto second spot in Division One West having completed a three-wicket triumph over Clifton Alliance 2nds, whom they sent packing for only 88.
Ian Twitchen bagged 4-18, while Will Bartlett (3-10) and Jamie Perkins (3-25) did their bit.