It can be used instead of the verb "to leave". For example:
A: "This party is really boring, right?"
B: "Yeah, shall we bail?" (Yeah, shall we leave?)
Or it can be used to say that someone didn't meet another person (but they planned/arranged to in the past). For Example:
A: Steve and I are going to the movie theatre tomorrow. Do you want to come?
B: Sure! See you then.
*The next day at the movie theatre*
B: "Where is Steve?"
A: "Ah, he bailed!" / "Ah, he bailed on us!" (Ah, he is not coming anymore!)
Hope this helps!