Because Christ's Apostle Paul commanded it:
1 Timothy 2:8 I desire therefore that the men pray everywhere, lifting up holy hands , without wrath and doubting.
Because King David, a man after God's own heart, set the example in the Psalms:
Psalms 28:2 Hear the voice of my supplications when I cry to You, when I lift up my hands toward Your holy sanctuary.
Psalms 63:3-4 Because Your lovingkindness is better than life, my lips shall praise You.
4 Thus I will bless You while I live; I will lift up my hands in Your name.
And King David would lift his hands, pledging allegiance to the Law of God:
Psalms 119:48 My hands also I will lift up to Your commandments, which I love, and I will meditate on Your statutes.
Because the Psalmist teaches that lifting our hands in the sanctuary blesses the LORD, who responds by blessing us:
Psalms 134 Behold, bless the LORD, all you servants of the LORD, who by night stand in the house of the LORD!
2 Lift up your hands in the sanctuary, and bless the LORD.
3 The LORD who made heaven and earth bless you from Zion!
Because King Solomon, son of David, in all his God-given wisdom, prayed this way, also:
1 Kings 8:22-23, 54-55 Then Solomon stood before the altar of the LORD in the presence of all the assembly of Israel, and spread out his hands toward heaven; 23 and he said: "LORD God of Israel, there is no God in heaven above or on earth below like You, who keep Your covenant and mercy with Your servants who walk before You with all their hearts....
54 And so it was, when Solomon had finished praying all this prayer and supplication to the LORD, that he arose from before the altar of the LORD, from kneeling on his knees with his hands spread up to heaven. 55 Then he stood and blessed all the assembly of Israel with a loud voice, saying: ...
Because our forefathers, the Old Covenant saints, even at their lowest, still remembered this standard posture for praying:
Isaiah 1:13-16 I cannot endure iniquity and the sacred meeting. 14 Your New Moons and your appointed feasts My soul hates; They are a trouble to Me, I am weary of bearing them. 15 When you spread out your hands, I will hide My eyes from you; Even though you make many prayers, I will not hear. Your hands are full of blood. 16 "Wash yourselves, make yourselves clean;
Because the prophet Jeremiah instructed praying so, even when contrite with repentance:
Lamentations 2:19 "Arise, cry out in the night, at the beginning of the [prayer] watches; pour out your heart like water before the face of the Lord. Lift your hands toward Him for the life of your young children, who faint from hunger at the head of every street."
Lamentations 3:40-42 Let us search out and examine our ways, and turn back to the LORD;
41 Let us lift our hearts and hands to God in heaven.
42 We have transgressed and rebelled; you have not pardoned.
Because Ezra the priest prayed this way, even in contrition for the sins of the Community:
Ezra 9:5 At the evening sacrifice I arose from my fasting; and having torn my garment and my robe, I fell on my knees and spread out my hands to the LORD my God.
Extra Observations - Why We Bow in Worship
A cursory concordance review of the Scriptures regarding worship reveal that "worship" is a wordless posture of surrendering oneself at the feet [of divinity, God, and His representative]. (Those verses can be visited later). Bowing one's head is a token effort towards this prostration. This is distinct from making prayerful petitions of God. Here are the few verses that refer to bowing one's head before God.
Because our forefathers, the Old Covenant saints, set the example:
Exodus 4:30-5:1 And Aaron spoke all the words which the LORD had spoken to Moses. Then he did the signs in the sight of the people.
31 So the people believed; and when they heard that the LORD had visited the children of Israel and that He had looked on their affliction, then they bowed their heads and worshiped.
Exodus 12:27 ... that you shall say,'It is the Passover sacrifice of the LORD, who passed over the houses of the children of Israel in Egypt when He struck the Egyptians and delivered our households.'" So the people bowed their heads and worshiped.
1 Chronicles 29:20 Then David said to all the assembly, "Now bless the LORD your God." So all the assembly blessed the LORD God of their fathers, and bowed their heads and prostrated themselves before the LORD and the king.
2 Chronicles 29:30 Moreover King Hezekiah and the leaders commanded the Levites to sing praise to the LORD with the words of David and of Asaph the seer. So they sang praises with gladness, and they bowed their heads and worshiped.
Notice how Ezra the priest guides these Old Testament saints to BOTH lift their hands in prayer then bow their heads in worship. Prayer and worship are different words and have different body language associated with each. "Love the Lord with ... all your body (strength)."
Nehemiah 8:5-6 And Ezra opened the book in the sight of all the people, for he was standing above all the people; and when he opened it, all the people stood up. 6 And Ezra blessed the LORD, the great God. Then all the people answered, "Amen, Amen!" while lifting up their hands. And they bowed their heads and worshiped the LORD with their faces to the ground.
I will show at a later time how worship is a posture of surrender, completely independent of words. Please let it suffice for now my recommendation that a concordance search of the words "worship" and "worshiped" will openly show that, no matter what is said or not, the common denominator is that the people surrendered themselves at the feet [of divinity, God] whenever they are described as in "worship" or having "worshiped."