ᠪᡳᡨᡥᡝ (bithe, “text; book”) + -ᠰᡳ (-si). Probably a phono-semantic matching of Mongolian ᠪᠠᠭᠰᠢ (baɣsi, “master, trainer, teacher”)
ᠪᡳᡨᡥᡝᠰᡳ • (bithesi)