I believe Benjamin Bailey came directly from London to Chaleur Bay after his 1774 marriage, and at least one of their children was born there:
Obituary of daughter Susannah Bailey Smith offers proof of Place of Birth
Charrie59 added this on 19 Feb 2013
Joan Davis and Janice Seeley's Sunbury County Happenings, Vol. 1, p. 7 contains the following from the Religious Intelligencer (Saint John, N.B.) of 25 Jul 1856: "Died At Blissville, Sunbury County, on the 15th inst., Mrs. Susannah, relict of the late Clapman Smith, Esq., in the 82nd year of her age, leaving 8 surviving sons and 2 daughters, with a large number of grand and great grandchildren. Mrs. Smith was born at the Bay Chaleur, to which her parents had emigrated from London. They removed to the Saint John River when she was about 4 years old. Her father was a truly pious and devoted disciple of Christ, and for many years sustained the public worship of God. When 17 years of age she was married to Mr. Smith, by whom she had 15 children; one died in infancy, another in early years, all the rest professed faith in the Savior. During the last 13 years she had been a widow, waiting for the time of her departure. During the last 2 or 3 years her faculties failed so far that at times she did not recollect her own friends, even her own children were sometimes forgotten by her, but at no time did she forget her Savior."