Hi, I don't know what to say. I've been before in Jordan and Egypt, but Palestine is much more civilized part of Arab world. Definitely is not recommended to travel with care rented with Israel plates, inside Palestine even if some place seems to be OK. I don't have recent information from Israel, but a lot of tourists from my country (Romania) are traveling in Israel, and in Jericho (seems that is a Romanian church there). The major roads, even inside Palestine (West bank) are full controlled by Israel and are very safety. I didn't stop inside of Jericho, except tourist places, but from the car the town was quiet and clean. It is a plate to the entrance of the town, where is mentioned that Jewish people, especially citizenship of Israel are not allowed to travel inside. At Hisham's Palace were no other tourists, but the place is somewhere not in the center. Jericho Tell is in center of Jericho, and tourists are welcomed. parking for Mount of Temptation was in a not very populated area, in my opinion very safety place. The road along Wadi Qelt is very spectacular and I recommend to stop in different places. I stopped in a view point on the opposite part of St. George's Monastery and some people ask us to buy some souvenirs. if you don't have problems with them is not a problem of security. Nabi Musa was very quiet at the sunset time. Overall there are no problems of security in Jericho area.
For Bethlehem I took an Arab bus from Jerusalem, Arab bus station in front of Damascus gate. Once again the bus was very clean and with a lot of tourists. In Bethlehem I choose to take a car in order to visit something outside. We negotiate around 240 shekel for Solomon's pools (I don't recommend), Herodion, Mar Saba Monastery and Deir Theodosius Monastery, all of them outside Bethlehem. At Solomon's pools that is on the road to Hebron I asked the driver to go also in Hebron. He asked me more 200 shekels, and I agreed. In Hebron the main attraction is Cave of the Patriarchs, that is UNESCO church divided inside by a wall in Jewish and Muslim parts. My trip was on Saturday. So, the Arab taxi will leave you in Arab part, and you have chance to visit their part of the church. If is prayer time, you have to wait. On Saturday (sabbath) for tourists is not allowed to visit Jewish part. Nearby is Shuhada street. Is controlled by Israel army, and you need to have the passport with you. It is little be creepy, but safety. it's part of the war. If some place is not recommended in current political situation, this part could be, but is Israel army at every 50 m.
I did'n visited other parts of Hebron, but if you have time and money I recommend to book a trip in Jerusalem for Hebron, that provide you half day jewish guide and half day muslim guide to discover the both stories.
From Hebron I moved to Herodion and Mar Saba Monastery. Inside Mar Saba women are not allowed, so my wife wait me outside. The desert landscape are very nice. On the way back to Hebron we stop at Deir Theodosius Monastery, but was closed. Our driver stop us at Shepherd Fields (nothing to see) and finally to Milk Grotto and Church of Nativity. I asked driver to go us also in Batir, UNESCO site near Bethelehm, but you need to know exactly where to stop. After all trip, the driver stop us in the meddle of nowhere, not very far from the border (and wall) between Bethlehem and Jerusalem. He asked my more that we negotiated (240 + 200 additional), because we asked to stop in other places; Shepherd Fields where I did'n asked, and Batir. I gave him around 50 shekels more (because Batir was in opposite side of Bethlehem) and he was not satisfied. I argued with him, and I asked him to drive us back to the bus station not to leave us on the road. He drove us to the bus station. I'm sure that now we can't be friends. So, my recommendation if you want to rent a taxi in Bethlehem is to establish very well all the stops, and to not agree to stop in places that you don't want to visit because they will try to charge you. if you choose to have more time in Bethlehem is perfect. The bus back to Jerusalem stop at checkpoint. All the locals have to go out from the bus, and all the tourist have to stay in the bus. The army will control you the passport/visa.
This is my story and I don't have an advice for you. After Jericho, Bethlehem, Hebron and Jerusalem our trip was in more safety places in hole Israel, except Golan Heights.
