(Jesus was born in Bethlehem:)

Luke 2:4 And Joseph also went up from Galilee, out of the city of Nazareth, into Judaea, unto the city of David, which is called Bethlehem; (because he was of the house and lineage of David:)

  6 And so it was, that, while they were there, the days were accomplished that she should be delivered.

(After 8 days Jesus was circumcised.

Then after 33 days more, they left Bethlehem to bring an offering to Jerusalem according to the law:)

Luke 2:21 And when eight days were accomplished for the circumcising of the child, his name was called JESUS, which was so named of the angel before he was conceived in the womb.

  22 And when the days of her purification according to the law of Moses were accomplished, they brought him to Jerusalem, to present him to the Lord;

(Only 41 days after Jesus was born, they left Bethlehem:)

Leviticus 12:2 Speak unto the children of Israel, saying, If a woman have conceived seed, and born a man child: then she shall be unclean seven days; according to the days of the separation for her infirmity shall she be unclean.

  3 And in the eighth day the flesh of his foreskin shall be circumcised.

  4 And she shall then continue in the blood of her purifying three and thirty days; she shall touch no hallowed thing, nor come into the sanctuary, until the days of her purifying be fulfilled.

  6 And when the days of her purifying are fulfilled, for a son, or for a daughter, she shall bring a lamb of the first year for a burnt offering, and a young pigeon, or a turtledove, for a sin offering, unto the door of the tabernacle of the congregation, unto the priest:

(Then they returned to Nazareth, not Bethlehem:)

Luke 2:39 And when they had performed all things according to the law of the Lord, they returned into Galilee, to their own city Nazareth.

(They were not in Bethlehem for two years.

The wise men came when Jesus was born, not two years later:)

Matthew 2:1 Now when Jesus was born in Bethlehem of Judaea in the days of Herod the king, behold, there came wise men from the east to Jerusalem,

(They had seen the star in the east, and they saw it in Jerusalem.

The star then went before them, moving southward, towards Bethlehem, then the star stopped moving and stood over where Jesus was:)

Matthew 2:2 Saying, Where is he that is born King of the Jews? for we have seen his star in the east, and are come to worship him.

  7 Then Herod, when he had privily called the wise men, enquired of them diligently what time the star appeared.

  9 When they had heard the king, they departed; and, lo, the star, which they saw in the east, went before them, till it came and stood over where the young child was.

(So why do some people say that the wise men came two years after Jesus was born?)

Matthew 2:16 Then Herod, when he saw that he was mocked of the wise men, was exceeding wroth, and sent forth, and slew all the children that were in Bethlehem, and in all the coasts thereof, from two years old and under, according to the time which he had diligently enquired of the wise men.

(The wise men first saw the star two years earlier, there are two explanations:

Like some teach, the wise men came to Bethlehem 2 years after the birth

Or, they saw the star, made arrangements to travel, then probably took the much longer fertile crescent caravan route,

rather than straight through the desert, possibly travelled slower at night to follow and/or look for the star:

all these things could very easily taken the two years mentioned)

(As seen above, Mary and Joseph were only in Bethlehem for 41 days.

Then they were in Jerusalem to present the offering in the temple.

After which, they were to return to Nazareth, according to:)

Luke 2:39 And when they had performed all things according to the law of the Lord, they returned into Galilee, to their own city Nazareth.

(However, something happened to prevent them from immediately returning to Nazareth:)

Matthew 2:13 And when they were departed, behold, the angel of the Lord appeareth to Joseph in a dream, saying, Arise, and take the young child and his mother, and flee into Egypt, and be thou there until I bring thee word: for Herod will seek the young child to destroy him.

  14 When he arose, he took the young child and his mother by night, and departed into Egypt:

  15 And was there until the death of Herod: that it might be fulfilled which was spoken of the Lord by the prophet, saying, Out of Egypt have I called my son.

  19 But when Herod was dead, behold, an angel of the Lord appeareth in a dream to Joseph in Egypt,

  20 Saying, Arise, and take the young child and his mother, and go into the land of Israel: for they are dead which sought the young child’s life.

  21 And he arose, and took the young child and his mother, and came into the land of Israel.

  22 But when he heard that Archelaus did reign in Judaea in the room of his father Herod, he was afraid to go thither: notwithstanding, being warned of God in a dream, he turned aside into the parts of Galilee:

  23 And he came and dwelt in a city called Nazareth: that it might be fulfilled which was spoken by the prophets, He shall be called a Nazarene.

(After they returned from Egypt, they avoided Judaea, i.e. Bethlehem and Jerusalem.

It seems that is when they finally got to Nazareth.)