1690s, "sculpture of upper torso and head," from French buste (16c.), from Italian busto "upper body," from Latin bustum "funeral monument, tomb," originally "funeral pyre, place where corpses are burned," perhaps shortened from ambustum, neuter of ambustus "burned around," past participle of amburere "burn around, scorch," from ambi- "around" + urere "to burn." Or perhaps from Old Latin boro, the early form of classical Latin uro "to burn." The sense development in Italian probably is from the Etruscan custom of keeping the ashes of the dead in an urn shaped like the person when alive.
From 1727 as "trunk of the human body above the waist." Meaning "bosom, measurement around a woman's body at the level of her breasts" is by 1884.
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Definitions of bustier from WordNet
a close-fitting and strapless top without sleeves that is worn by women either as lingerie or for evening dress;