Originally, the verb "to bail" meant to remove water from a boat using buckets. From that it came to mean jumping out (parachute) of an airplane, and more generally to escape from any unwanted situation that you want to escape.

"Let's leave." Let's leave this party, let's leave this event, let's leave this meeting. "Bail" is short for the phrasal verb "to bail out," which can mean "to jump out of an airplane with a parachute." "Let's bail" carries the idea of being bored. It can mean to "escape" from a party or an event, even though you were expected to stay until the end.