The River House at the Swinging Bridge Address: Madison, Virginia Madison , VA 22727 Website Place Category: Airbnb & Cabin Rentals The River House at the Swinging Bridge is a 13 acre property which includes a 2 acre fenced compound ideal for gatherings of families or friends. Loading... No Records Found Sorry, no records were found. Please adjust your search criteria and try again. Maps failed to load Sorry, unable to load the Maps API. Enter your locationGet Directions Travel modeDrivingWalkingBicyclingPublic Transport Distance unitsMilesKilometers