In the example, verb bail is being used more along the lines of “To fail to meet a commitment” rather than either of the alternatives you mentioned.
Something I associate with bailed or bailed on me or bailed out on me is being told at the last minute that the person can't make it. If they just don't show up, and don't tell you, they have stood you up instead of just bailing. However, I don't know if that's a common interpretation of the connotations.
The sense “To fail to meet a commitment” of bail, and the other senses you mentioned, ultimately stem (I think) from the following sense:
2. To admit to bail, to liberate on bail; to release
(a person) from immediate arrest or imprisonment,
on security being given by one or more sureties
that the person so released shall be duly presented
for trial. (From OED1's entry for verb bail; with cites from 1548 forward)
In a comment, J.R. suggests that bail's sense of abandoning an obligation is associated with boat-bailing rather than with freeing from arrest, and provides a collinsdictionary link in evidence. Note that that link makes no explicit connection between boat-bailing and obligation-abandoning, but merely includes a link to a bail out entry that includes the sense “(informal) to flee a difficult or dangerous situation”. However, etymonline's bail entry is very slightly more explicit; within the item that refers to boat-bailing it says: “To bail out "leave suddenly" (intransitive) is recorded from 1930, originally of airplane pilots”.
Bail (v.1, 1610s), as in to bail a boat, derives from nautical Old French baille “bucket, pail”.
Bail (v.2, 1580s), as in to bail someone out of jail, derives from Old French baillier “to control, to guard, deliver”.
Both Old French terms derive from Latin bajulare “to bear a burden”.