Nazareth and Bethlehem are almost directly north and south of one another in the center of Israel. there's a highway there now (#60) that connects them but Mary and Joseph would be wise to avoid that road since it runs through Samaria, now major Palestinian territory (think Ramallah).
Today, like then, you have to pass through Jerusalem to get to Bethlehem. It's about 80 miles on #60 from Nazareth to Jerusalem, and less than 10 more to Bethlehem.
I have almost no doubt that Joseph and Mary would have taken a longer way to get there. They would have gone east to the Jordan River (safer, not to mention cooler/easier to be near the water) then walked south, then west to Jerusalem, adding about 30 miles to their trip.
I'd guess they walked about 120 miles.
pregnant on a donkey
also, the altitude would get lower as they walked south towards the Dead Sea (where the Jordan River ends) but entering Jerusalem would be a bit of a hill