How exactly such an investment deal might work and what the authority would do — or legally could do — with the money is unsettled, despite a two-hour meeting. Even the language of the bid solicitation is uncertain. The proposal affects a broad area of southern Cumberland County. The authority is a regional sewerage system provider, with contracts with Bridgeton and the townships of Upper Deerfield, Hopewell, Deerfield, and Fairfield. The authority also has contracts with TIP’s Trailer Park in Fairfield and the Federal Correctional Institution at Fairton, and it has serviced county buildings including its technical school. On Thursday, authority commissioners grudgingly listened to a representative of the private equity firm Bernhard Capital Partners. Ron DeGregorio previously had met the authority’s three-member Finance Committee and the CCUA legal counsel.