Stow took charge with the ball, cleaning up the tail en route to figures of 5-23 as Bridge were dismissed for 131.
Replying, Good (60) and Tattersall (51) put on 97 for the second wicket as Gate claimed victory with 20 overs to spare.
Academy (194) made it five wins in a row, but missed out on maximum points against Hull (178-7).
Mosun Hussain top-scored with 43, and James Logan (4-51) and Jordan Thompson (3-39) were in the wickets.
A century partnership between Duncan Snell (79no) and Alex Collins (43no) helped York (175-3) move up to fourth with victory over Driffield Town (173).
Dan Woods (4-51) and Tom Pringle (3-56) helped curtail Driffield’s progress.
Scarborough (194) continued their upturn at the expense of Castleford (154).
David Wainwright continued his purple patch with 54 for Cas, supported by Connor Hyde (43) while Eddie Morrison took 5-44.
Wakefield Thornes saw off Sheffield Collegiate by the Duckworth-Lewis method, despite a fine 127 from Will Root, brother of Yorkshire and England’s Joe.
David Toft hit 46 not out for Thornes.