Do we know the dates of the Roman Census ordered by Augustus? Married couples had to go to the home town of the man.
Bethlehem was only a couple of miles from Jerusalem and was where the Temple raised all their lambs for slaughter. Bethlehem means "House of Bread" ergo Jesus is the Bread of Life. He was the Lamb of God, so it was fitting He was born where the lambs came from.
I think the one in 7BC is probably the one referenced but that is just my opinion and not to be confused with that of anyone who matters.