Bowing is not worship.
Bowing to another person is giving honour, respect to them.
This is why God cut off the tribe of Dan and Ephraim as they never repented from bowing down and worshiping those things made by hand that became their idols of worship. Gods word does not come back to Him void, but it shall accomplish that which He pleases, Isaiah 55:10, 11.
These are but only a few scriptures about only bowing down and worshiping God and His Son Christ Jesus. Mary is never mentioned in the doctrines of Christ, but only the doctrines of the Catholic Church through the catechism.
Exodus 20:4 Thou shalt not make unto thee any graven image, or any likeness of any thing that is in heaven above, or that is in the earth beneath, or that is in the water under the earth:
Exodus 20:5 Thou shalt not bow down thyself to them, nor serve them: for I the LORD thy God am a jealous God, visiting the iniquity of the fathers upon the children unto the third and fourth generation of them that hate me;
Leviticus 26:1 Ye shall make you no idols nor graven image, neither rear you up a standing image, neither shall ye set up any image of stone in your land, to bow down unto it: for I am the LORD your God.
Psalms 95:6 O come, let us worship and bow down: let us kneel before the LORD our maker.
Isaiah 42:8 I am the LORD: that is my name: and my glory will I not give to another, neither my praise to graven images.
Jeremiah 7:15 And I will cast you out of my sight, as I have cast out all your brethren, even the whole seed of Ephraim.
Jeremiah 7:16 Therefore pray not thou for this people, neither lift up cry nor prayer for them, neither make intercession to me: for I will not hear thee.
Jeremiah 7:17 Seest thou not what they do in the cities of Judah and in the streets of Jerusalem?
Jeremiah 7:18 The children gather wood, and the fathers kindle the fire, and the women knead their dough, to make cakes to the queen of heaven, and to pour out drink offerings unto other gods, that they may provoke me to anger.
Jeremiah 7:19 Do they provoke me to anger? saith the LORD: do they not provoke themselves to the confusion of their own faces?
Jeremiah 7:20 Therefore thus saith the Lord GOD; Behold, mine anger and my fury shall be poured out upon this place, upon man, and upon beast, and upon the trees of the field, and upon the fruit of the ground; and it shall burn, and shall not be quenched.
John 14:13 And whatsoever ye shall ask in my name, that will I do, that the Father may be glorified in the Son.
1 Timothy 2:5 For there is one God, and one mediator between God and men, the man Christ Jesus
Hebrews 7:25 Wherefore he is able also to save them to the uttermost that come unto God by him, seeing he ever liveth to make intercession for them.
Rev 19:10 And I fell at his feet to worship him. And he said unto me, See thou do it not: I am thy fellowservant, and of thy brethren that have the testimony of Jesus: worship God: for the testimony of Jesus is the spirit of prophecy. (Mary was also a fellowservant, handmaiden, like all of us women who serve God.)