…which means that the Virgin could have well traveled there within a week (note St. Luke’s “with haste”) or even sooner, if by burro.
Given the circumstances, I doubt that she would have traveled alone due to the criminal elements and Jewish cultural ethics.
…as for John the Baptist, God had visited the parents and made exact conditions on how the child was to be brought up:
[FONT=“Garamond”][size=]15 For he shall be great before the Lord; and shall drink no wine nor strong drink: and he shall be filled with the Holy Ghost, even from his mother’s womb.
(St. Luke 1:15)
Zachariah was not only part of the priesthood but also of Israel’s Remnant so it is very likely that knowing that John was part of a special covenant with Yahweh he would have been sent to a desert community (as with other prophets of God)–much like cloistered Nuns and Monks–where he would grow up in the service of the Lord.
…Elizabeth recognized the Virgin as the mother of her Lord because John was filled with the Holy Ghost/Spirit right from his mom’s womb (above) and:
43 And whence is this to me, that the mother of my Lord should come to me? 44 For behold as soon as the voice of thy salutation sounded in my ears, the infant in my womb leaped for joy.
(St. Luke 1:43-44)
The Holy Spirit came upon Elizabeth and she was able to Know about God’s Design!
Elizabeth and Mary may well have visited each other… but remember, most likely, John is not living with his parents; John’s parents were quite old, past their eighties… which means they could well have passed soon after John’s birth.
Back in those days there were often caravans moving from town to town. Mary most likely traveled with one of the caravans that was going to Elizabeth’s town, as it is extremely unlikely she went alone.
How did Elizabeth know that Mary was carrying the Messiah?
Because of the prophecy (Luke 1:15). When John leapt in her womb, she knew it was Mary’s child.
Why didn’t Mary and Elizabeth visit each other again as it seems John the Baptist didn’t know Jesus by sight when they met?
“Lowercase t” tradition says that Elizabeth was much older than Mary, perhaps the age of Mary’s parents or even grandparents. After Jesus was born, Jesus, Mary & Joseph left for Egypt from Bethlehem and lived there for of a while. Some believe that Elizabeth and Zachariah may have died when Mary was gone or before they had the opportunity to see each other again. Furthermore, tradition says that John was sent away to learn the scriptures, etc, perhaps because his parents died. Some scholars believe John was studying and living with the Essenes.