Why do Catholics bow for icons of the Virgin Mary? It doesn't surprise me when orthodox Christians bow for icons of the Virgin Mary, since they believe that she is present in the icon. But why do (some) Catholics also bow for icons of Mary?

There are numerous pages on the internet like this one where the author argues against this gesture. The reasoning is that it's against the commandment from Ex 20:4-5:


  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: 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.


However, I cannot find arguments against this position. I guess there are, but what are they?
First off, Catholics do not believe Mary is "present in the icon" in the same way we believe Jesus is present in the Eucharist in a particularly physical way (the Eucharist, or physical incarnation of Jesus on Earth, is the only actual physical thing that Catholics worship to my knowledge). Though Mary, like all the other saints (and of course our omniscient God the Father, Son and Holy Spirit), have the power to be present in the world with us, she is not uniquely present in an icon.

Also keep in minds that Catholics do not worship Mary. Worship is reserved only for God, the Holy Trinity. Mary is still a human like us, but also a saint, and she is the most highly revered of all the saints because she represents the perfect model of a Christian fidelity through God's gift to her of being born without original sin, and by her perfect example of obedience to God's will as evidenced in the Bible (you can find more info on that topic here).

So why do we bow, kneel before, or what is better known as "venerate" icons of the Blessed Virgin Mary (or to other icons for that matter)?

An icon is distinct from an idol in that one does not worship the icon or image, but recognizes that it helps us as mortals keep our minds fixed on our prayer toward God through the saints (or Mary in this instance). To expand on this, we believe that Mary, as the only mother of God, has a unique relationship with her son that allows her to intercede for humans in the outpouring of God's graces. We honor Mary and other saints because they are already in Heaven and have this power to intercede for us in a unique way, though one must keep in mind that Mary and the saints have absolutely no power on their own, and that all power and graces come from God.

Icons are symbols or reminders of these facts and serve to help us stay in a holy frame of mind in a similar way to how music enhances our liturgical worship. So though icons are not necessary for prayer, they can be worship aids that greatly enhance our perception of God and the saints among us. This could be extended in a loose sense to why we like to make churches beautiful: to remind us that God is with us and that He is beautiful to the greatest extreme. But no matter what, icons should never, ever become objects of worship- that is idolatry.

Certain icons/images have a more important distinction among the faithful through their miraculous or supernatural origins, Our Lady of Guadalupe  being one such famous example. Because of this, they are generally considered greater representations and reminders of God's greatness and His power to elevate the saints, especially Mary, as models and intercessors for us.

So to answer your question, Catholics bow to images/icons of Mary not because she is present in them, but because of what they represent: the fact that Mary holds the highest position among the saints and her unique role of intercessor for humans. The images are reminders of this fact.

Please keep in mind, my say is not the final say by any means, and there is much more to the theology behind the practice of veneration of images, so I would recommend to do a bit more research if you still have questions (or leave comments and I'll do my best).