Green’s Dictionary of Slang

budge n.3

[? abbr. SE budget, a pouch, bag, wallet, usu. of leather]

(US) a woman’s breasts.

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[US]J. Ciardi A Second Browser’s Dict. 34: Budge. A woman’s bosom, esp. the brassière encasing it and conceived as a sack or pouch for storage or safekeeping of small objects. She slipped (stuffed) the double sawbuck into her budge.