Dorset, where she was Countess, is located just south of Somerset where Bath and the Holburne Museum is located. Bath has been a health spa destination for millennia and Roman water works can be seen by tourists today. It may be that the gold pin on her bodice was made over a thousand years before she wore it for this portrait.
Her article in thepeerage.com follows, "Mary Bagot was born in 1645. She married, firstly, Charles Berkeley, 1st Earl of Falmouth, son of Charles Berkeley, 2nd Viscount Fitzhardinge of Berehaven and Penelope Godolphin, on 18 December 1664.1 She married, secondly, Charles Sackville, 6th Earl of Dorset, son of Richard Sackville, 5th Earl of Dorset and Frances Cranfield, in June 1674.1 She died on 12 September 1679.
She was the daughter of Hervey Bagot and Dorothy Arden.1 From 18 December 1664, her married name became Berkeley. From June 1674, her married name became Sackville."