Arthur Weise has one of the few descriptions I’ve found of the former village of Bath-on-the-Hudson:
“Bath-on-the-Hudson, the first station on the Troy and Greenbush Railroad, three miles south of the city [of Troy]. It derived its name from several mineral springs, discovered about the close of the last century, near the village. John Maude, an English traveller, in June, 1800, visited the place; which he described as a ‘town lately laid out by the patroon,’ and having ‘about thirty houses,’ ‘The medicinal springs and baths, at one time so much vaunted, are now shut up and neglected; yet, as a watering place, it was to have rivaled Ballstown, and, as a trading place, Lansingburgh and Troy.’ The manor-house, north of the village, was built about the year 1839, by William P. Van Rensselaer. The village was incorporated May 5, 1874.”
Weise wrote that in 1888. The City of Rensselaer was incorporated in 1897, absorbing Bath, Greenbush, and East Albany. Rensselaer’s website describes the boundaries of the old Village of Bath-on-the-Hudson as “Hudson River (west); Washington Avenue and peripheral street (north);
Quackenderry Creek gorge (east); Catherine Street vicinity (south).”