Hi Mandy, I can't specifically answer your question pertaining to this couple.However, with regard to the name of Bates, the following might give you an idea of where to go for more info.Might be connected - might not.I got this information from "Burke's Colonial Gentry."
"Thurston, His Excellency Sir John Bates, KCMG, FRGS, FLS, of St. Helier's Taviuni; Thornbury, Viti Levu; and Government House, Suva, all in Fiji, governor and commander-in-chief of the colony of Figi, and HBM's high commissioner and consul-general for the Western Pacific, b. 31st January, 1836; entered the British Consulate at Fiji and Tonga, 1866; acting consul, 1867; chief secretary and minister for foreign relations, 1872, elected 'chosen and special adviser' of the native kings and chiefs to confer with H.M. commissioners regarding the annexation of the islands to Great Britain, 1874; colonial secretary and auditor-general of the colony, 1874; secretary to H. M. high commissioner for the West Pacific, 1879; administered the government of Fiji, 16th November to 20th December, 1880, 10th November, 1883, to 23rd July, 1884, and again in 1885--6; consul-general for the Western Pacific Islands, 1888; lieutenant-governor, 1886, and governor, 1887.He m. 14th January 1883, Amelia, only daughter of John Berry, Esq. of Albury, New SouthWales, and formerly of Co. Meath, Ireland (see Berry of SUVA)................
the ancestors of this family settled at Kingston, Thornbury, county Gloucester, England, a copyhold belonging to the Duke of Buckingham.The family, of which there are still many branches existing, is one of the oldest in Gloucestershire, and has now been seated at Kington House for nearly five centuries.The Suffolk family of Thurston, like the Kentish line, is now extinct, and it is believed that these, the Thurstons, of Gloucestershire, are the only direct descendants of John Turstin, the branches of whose family in counties Norfolk, Suffolk, and Kent called themselves Turstin, Thurston, and Thruston, and in the western counties assumed the name of Basset."