Opening batsman and captain Simon Belston top-scored with 27 as Bury looked to take advantage of the washout game between leaders Flixton and second-placed Daisy Hill at Lostock on Saturday.
Mukthar Nasir also hit 22 at Haydock as the hosts notched up 132 off 37.1 overs.
David Flanagan took 5-47 off his 14 overs which included five maidens and Robert Holgate took 3-36.
In reply, Jordan Belston took 2-2 as Lostock managed to post 43-4 off 18.4 overs before the game was abandoned due to rain, with Peter Flanagan the top scorer on 18 not out.
There was no play in Elton’s fixture with Worsley and Blackrod’s match against Walshaw was cancelled without a ball being bowled.
l In the Bolton League, Greenmount’s game against Astley Bridge was also called off.