Duke Street's expected deal with the the leisure group values the 28 Superbowl alleys at pounds 110m. The package also includes Trecco Bay in Wales, Britain's largest caravan park, and the Snowdome indoor ski-slope in Tamworth, Staffordshire.
Bass had previously been expected to acquire the businesses with a knockout bid of pounds 115m just for the bowling alleys. But its interest is thought to have waned due to the distraction of its involvement in Punch Taverns' bid for Allied Domecq's pub estate.
The winning bid has seen Duke Street team up with Allied Leisure, the bowling-to-Burger King group that recently secured a merger with rival European Leisure.
Sources close to the deal suggest that it was the involvement of Allied, whose team will run the businesses, which helped secure Duke Street's victory at the expense of a rival bid from 3i, the Manchester-based venture capitalist.
Duke Street's triumph is the latest in a series of leisure coups for the company. Its most recent deal came in March with the pounds 30m acquisition of Stretton Leisure, the fruit machine business previously owned by Greenalls. Duke Street's other big deal this year was the pounds 42m sale in January of Country Hotels to Regal Hotels.
Duke Street, based in St James's in West London, was spun off last year from Hambros and is run by Edmund Truell.
The sale is the latest stage of First Leisure's quest to reinvent itself as a dedicated operator of health and fitness clubs.
The company has already sold off its bingo halls and a resorts division, which included the Blackpool Tower. Its nightclubs and bars arm is also up for sale.
The deal will hasten the departure of First Leisure's chief executive Michael Grade, who is to stand down in favour of Graham Coles, currently the company's finance director.
Mr Grade is expected to step down once he has sold off First Leisure's nightclubs and bars.
However Mr Grade's break-up plan has incurred the wrath of his aunt, Lady Delfont, the widow of First Leisure's founder. She accused her nephew of "asset stripping' the company. First Leisure was founded in 1982 when Lord Delfont, then 72, staged a management buyout of Trusthouse Forte's leisure business.