A budget was, originally, a little leather pouch in which you carried your money. The word first popped into English in the fifteenth century. Before that it was living in France as bougette, a diminutive form of bouge, or leather bag. Bouge came from the Latin bulga, which also meant leather bag.
However, the Norman French took that Latin bulga on in a different way. They had boulge. And from that the English, in about 1200 got the word bulge. Bulge also meant leather bag, but soon it started to mean... well... bulge.
However, when sailors referred to the bulge of a ship's hull, they called it a bilge. Then, when sailors referred to the nasty rotten water that collected at the bottom of a ship's hull, they called that bilge water, or just bilge.
None of which has anything to do with Bulgarians.
I should probably mention that, as ever, the Inky Fool has no political opinions and believes in government by whim.
Or it may be a small budgerigar.