There's a bus from Amman to Nazerath 3x/weekly if that's helpful!
https://abrahamtours.com/tours/trans...-amman-jordan/
If the direct bus isnt possible crossing the border you can get dropped off on the Jordanian side either by taxi or shuttle bus from Irbid(Change from Amman bus there) Then it's a shuttle bus (1 JD when I last took it) across the no man's land into Israel. The Israelis will board the bus as soon as you cross. You then arrive at the Israeli terminal. The last time I did it they were very curious why I went to Jordan and also why I didn't fly from AMM.. When you arrive in Beit Shean it's the middle of no where. Last time I took a taxi from there, but there is a bus service as well except on Shabbos. Hope this was helpful!
Cheers
Howie