If you want to go to Bethlehem from Jerusalem, you can simply watch out for a Palestinian taxi at the Damascus gate. Or if you are travelling by rental car you can enter the most important border crossing into your GPS: checkpoint 300. At this point you can park your car and get via taxi to the town – but be sure to negotiate the price before the ride.
Going from Jerusalem to Bethlehem is no-frills: the taxi driver simply has to show his identity card. On the way back you have to give your visa to the IDF and the car trunk will be checked. Going this way is quite fast in low season, elsewise you might experience some queues during border control.
Travelling between these two worlds also gives you the experience of a close view on the wall built between Israel and the Palestinian autonomy areas. It immediatly reminds you on the Berlin wall. And hopefully this one will be torn down in the future, too.