[A figurative application of toast n.1, the name of a lady being supposed to flavour a bumper (A cup or glass of wine, etc., filled to the brim, esp. when drunk as a toast.) like a spiced toast in the drink.
See the Tatler, No. 24, of 2 June, and No. 31, of 18 June, 1709, in both of which toast is explained as a new name, upon the origin of which ‘the Learned differ very much’. No. 24 says that ‘many of the Wits of the last Age will assert’ that the term originated in an incident alleged to have occurred at Bath in the reign of Charles II, 1660–1684. No. 31 is silent as to the incident, and gives the account cited below.]

1709 Steele Tatler No. 24 39 This Whim gave Foundation to the present Honour+done to the Lady we mention in our Liquors, who has ever since been called a Toast. Ibid. No. 31 38 Then, said he, Why do you call live People Toasts? I answered, That was a new Name found out by the Wits to make a Lady have the same Effect as Burridge in the Glass when a Man is drinking. Ibid. No. 71 38 A Beauty, whose Health is drank from Heddington to Hinksey,+has no more the Title of Lady, but reigns an undisputed Toast.