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1 Samuel 1 21The man Elkanah and all his house went up to offer to the LORD the yearly sacrifice and to pay his vow. 22But Hannah did not go up, for she said to her husband, "As soon as the child is weaned, I will bring him, so that he may appear in the presence of the LORD and dwell there forever." 23 Elkanah her husband said to her, "Do what seems best to you; wait until you have weaned him; only, may the LORD establish his word." So the woman remained and nursed her son until she weaned him. 24And when she had weaned him, she took him up with her, along with a three-year-old bull, an ephah of flour, and a skin of wine, and she brought him to the house of the LORD at Shiloh. And the child was young. 25Then they slaughtered the bull, and they brought the child to Eli. 26And she said, "Oh, my lord! As you live, my lord, I am the woman who was standing here in your presence, praying to the LORD. 27For this child I prayed, and the LORD has granted me my petition that I made to him. 28Therefore I have lent him to the LORD. As long as he lives, he is lent to the LORD." And he worshiped the LORD there.

Judges 13 1And the people of Israel again did what was evil in the sight of the LORD, so the LORD gave them into the hand of the Philistines for forty years. 2There was a certain man of Zorah, of the tribe of the Danites, whose name was Manoah. And his wife was barren and had no children. 3 And the angel of the LORD appeared to the woman and said to her, "Behold, you are barren and have not borne children, but you shall conceive and bear a son. 4Therefore be careful and drink no wine or strong drink, and eat nothing unclean, 5for behold, you shall conceive and bear a son. No razor shall come upon his head, for the child shall be a Nazirite to God from the womb, and he shall begin to save Israel from the hand of the Philistines." 6Then the woman came and told her husband, "A man of God came to me, and his appearance was like the appearance of the angel of God, very awesome. I did not ask him where he was from, and he did not tell me his name, 7but he said to me, 'Behold, you shall conceive and bear a son. So then drink no wine or strong drink, and eat nothing unclean, for the child shall be a Nazirite to God from the womb to the day of his death.'"

Legend has it that Mary was dedicated to God by her parents.

You'll have to try again to demonstrate that it's an extra-Biblical practice.

The man Elkanah …
… certain man of Zorah …

You'll have to try again to demonstrate that it's an extra-Biblical practice.

All you have managed to do is point out a couple one-time events. There is no general mandate or command anywhere in the Bible for believing parents (Jewish or Christian) to observe these unique practices. Did you sacrifice a bull? Do you plan to leave your child at the temple and return home? Did you have a visitation from an angel regarding your barrenness? Obviously not, so your “dedication” is merely a human invention, fashioned after an out-of-context “application” of Scripture.

In that sense the practice is quite extra-biblical and follows no divine mandate. It is a tradition of men.