Named after Captain C.H. Bagot, MLC (1844-1869). Born in Ireland in 1788, he arrived in the Birman in 1840. He was an appointed member of the Nominee Legislative Council in 1842 and was later representative for the Light District from 1851 where he farmed near Shea-oak Log. He was also an agent for Sir Montague Chapman of Killen Castle who sent out 213 of his tenants rendered homeless by enclosures in Ireland to be under the direction of Captain Bagot.
Bagot Well is a locality north-east of Kapunda and on the road to Eudunda. It was named for Captain Bagot who owned a great deal of property in the area.
Bagot Well as a place began as a well sunk by Captain Bagot which became available for public use in 1855. On 5 December 1940, it was renamed from Bagot's Well to Bagot Well. On 16 March 2000, boundaries for the locality were created for the "long established name."
Bagot Well was served by the Morgan railway from when it was extended from Kapunda in 1878. The line closed in 1994, but passenger service had ceased much earlier and freight trains carrying bulk grain from Eudunda to Port Adelaide did not stop there.