If, as Luke's Gospel says, Joseph and Mary travelled from Nazareth to Bethlehem where Jesus was born, they both walked all the way. As a poor village carpenter, Joseph could not have afforded to own or even hire a donkey. Their extreme poverty is demonstrated in Luke 2:24, when they sacrificed two doves instead of the usual lamb, a concession permitted only the very poorest. Even if they knew someone of outstanding generosity, no one would have lent them a donkey, with the serious possibility that Joseph and Mary would not have survived the long and arduous journey to and from Bethlehem.

Although the Gospel does not say, the only plausible answer in the context of Luke's Gospel is that Joseph and Mary both walked, even on the return journey when they carried Jesus.