There are two towns named Bethlehem in the Holy Land.
Tradition places the site of Jesus' birth in Bethlehem near Jerusalem, which currently sits in the Palestinian territory. A journey here from Nazareth would have taken weeks; not the kind of trip for a woman about to give birth to take.
There is another town named Bethlehem right next to Nazareth, about two days journey to the Northwest. It is more likely that it was this Bethlehem, not the more famous one to the South, where Jesus was born.
This map was made in 2009 and shows some well known sites in the Holy Land.