Cyrus H. Gordon provides transliterations of Ugaritic texts (1350-1150 BC) that contain the term "glad tidings" (bšr) being used in religious contexts.
Cyrus H. Gordon, Ugaritic Textbook (Analecta Orientalia 38; Rome: Pontificium Institutum Biblicum, 1965), 172, 183, 245
[51:V]
[88] gh.wtṣḥ.tbšr b'l
[89] bšrtk.yblt.ybn
. . .
[76:III]
[34] bšrt.il. bš[r b]'l
[35] w bšr.ḥtk.dgn
. . .
[1 Aqht]
[86] abšrkm dn[ ]
. . .