Natural Bridge is a hamlet and census-designated place in Jefferson County, New York, United States. As of the 2010 census it had a population of 365. It is located in the northeastern corner of the town of Wilna and is east of Watertown. The name "Natural Bridge" was derived from Natural Bridge Caverns, marble cave which the Indian River run…Natural Bridge is a hamlet and census-designated place in Jefferson County, New York, United States. As of the 2010 census it had a population of 365. It is located in the northeastern corner of the town of Wilna and is east of Watertown. The name "Natural Bridge" was derived from Natural Bridge Caverns, marble cave which the Indian River runs underground through. Natural Bridge Station is a location along a railroad line southeast of the community in Lewis County.