Cyrus H. Gordon discusses Ugaritic bšr; defines it as "to get tidings (good or evil)," sometimes in a religious context.
Cyrus H. Gordon, Ugaritic Textbook (Analecta Orientalia 38; Rome: Pontificium Institutum Biblicum, 1965), 377
535. bšr II ‘to get tidings (good or evil)’ (76:III:34, 35); D ‘to bring tidings’ (1 Aqht 86); bšrt (76:III:34) ‘tidings’ ; (51:V:88) tbšr b'l (89) bšrtk.yblt ‘be informed, O Ba'l, I bring thy tidings’. בַּשֵּׂר 'to bring tidings (good or evil, cf. 1 Sam. 4.17)