No, Bethlehem is in Israel. The “West Bank” is an invention of leftists.
I understand what you are saying and totally agree with you that areas like the "West Bank" and the "Gaza Strip" in all rights should be part of Israel and we like to think of them as still Israel, however Israel was coerced into ceding in so called peace treaties, these areas to control of the Arabs who call themselves the Palestinians. The terrible reality is that there ARE border checkpoints into and out them.