c.1200, "wallet, leather bag," from Old French bouge, boulge "wallet, pouch, leather bag," or directly from Latin bulga "leather sack" (see budget, n.). Sense of "a swelling" is first recorded 1620s. Bilge, q.v. might be a nautical variant.

"to protrude, swell out," 1670s, from bulge, n.. Related: Bulged; bulging.