People have been bailing out sinking ships for thousands of years. They've only been bailing out of disabled aircraft for about a hundred years. Early aviators probably just adopted the pre-existing nautical term instead of inventing their own.

It's somewhat ironic that the two terms don't at all mean the same thing. The aim of a nautical bail out is to save the ship as well as the lives of the passengers and crew. The aim of an aircraft bail out is to save the lives of the crew only. (If there were any passengers on board, there probably wouldn't be enough parachutes to go around anyway.) The nautical term for the procedure analogous to bailing out of an air plane is "abandoning ship".

The supposed objective of a financial bailout is to save the ship, primarily for the benefit of its passengers, not its crew. That crew has probably already bailed out, in the aviation sense of the term, leaving someone else to bail out the ship, in the nautical sense.