Did you find anything on the Roman bath?
Just tenuous stuff
https://gardenandgun.com/articles/secrets-biltmore-estate/
Vanderbilt hired Hunt, an accomplished architect responsible for a handful of Vanderbilt residences in the Northeast. Vanderbilt and Hunt traveled together to England and France to gather design inspiration, paying particular attention to Waddesdon Manor in Buckinghamshire and several sixteenth-century chateaux in the Loire Valley.
https://en.wikipedia.org/wiki/Waddesdon_Manor
Waddesdon Manor is a country house in the village of Waddesdon, in Buckinghamshire, England. It is located in the Aylesbury Vale, 6.6 miles (10.6 km) west of Aylesbury. The Grade I listed house was built in the Neo-Renaissance style of a French château between 1874 and 1889 for Baron Ferdinand de Rothschild (1839–1898) as a weekend residence for grand entertaining and as a setting for his collection. The last member of the Rothschild family to own Waddesdon was James de Rothschild (1878–1957).