If you have time on your hands and it’s something you must do, Bethlehem is a half-day trip (from 8:30am-1:00pm) with an organised tour group. Have your passport handy, as you may need it at the checkpoint into the Palestine region. 

Bethlehem is located about 10km from Jerusalem. The area is run-down and there is not much else to do and see besides from the Church of Nativity, which was built around the cave where Jesus was born and then put to lay in his manger. 

With the many tour groups visiting this place, it means extensive waiting times. So if waiting around for an hour or so, to see the birthplace for all of about 20 minutes, is something you’re willing and must do, then go for it. Otherwise it could be missed and not regretted - but I guess it’s a good to see, once in your life.