When the time was near for Mary to give birth

This could mean ‘When it was near the end of Mary’s pregnancy.’

They had to go there because the Roman officials wanted to count all the people in the land of Israel. They wanted everyone to go to where their ancestors had lived. King David had been born in Bethlehem, and he was the ancestor of both Mary and Joseph.

This is background information about why Joseph and Mary had to travel to Bethlehem. (See: rc://en/ta/man/translate/writing-background)

Rome had conquered and ruled over Israel at this time.

This could mean ‘to write their names on a list.’ They probably did this so they could tax the people.