Whether they flat out admit that they worship Mary, as did Pope John Paul on the Vatican Information Service in 1997, attempt to dress it up, as most Catholics do, or simply aren't aware of all Catholic doctrines on Mary, one cannot deny that, to Catholics, Mary is a very important figure.
Of course, she's an important figure in Christianity too. A humble servant of God, Mary is the vessel through whom the Lord chose to give birth to Jesus, and is the virgin prophesied in the Old Testament. But Biblically speaking, this is as significant as she gets. She is a very blessed, yet otherwise barely significant (for lack of better term) woman. The Bible does not "venerate" her, nor does it command Christians to do so. In fact, after the first chapter of Acts, she drops off the map completely.
There is neither sign nor whisper of veneration of Mary in the New Testament. In fact, there are several passages in both Old and New Testaments that demolish the foundations for Mary being "Queen of Heaven" (Jeremiah 7:18; Jeremiah 44:17-25) or "co-redemtrix" (1 Timothy 2:5), and indeed the very concept of communication with the dead is considered an abomination signifying the absence of light in a person (Deuteronomy 18:10-14; Isaiah 8:19-20).
But aside from some very clear condemnations of Catholic Mariology, we actually have some visible examples of Jesus doing exactly what Catholics wouldn't. An example can be seen in Matthew 12, when Mary (and Jesus' brothers, because contrary to Catholic doctrine, He had those) came looking for Him. His response was to practically blank Mary in favour of His ministry, claiming that His mother and brothers were those who did the will of God.
Can you imagine a Catholic doing that? They fall prostrate to mere statues of Mary, so of course they wouldn't ignore her if she actually came looking for them. Apparitions of Mary are even used as evidence of the Catholic faith (Deuteronomy 13:1-3, by contrast, confirms that false prophets can do miracles, and 2 Corinthians 11:13-15 confirms that Satan and his apostles are capable of brilliant tricks and disguises, so even if an apparition genuinely did occur, claiming to be Mary, one must necessarily conclude that they are fake). So we know there's no way a good Catholic would just wave Mary off.
What's even more astonishing is in Luke 11, when a young woman cried out to Jesus "Blessed is the womb that bore You, and the breasts which nursed You!" (v27). This is significant. Catholics use Luke 1:48, wherein Mary says "...henceforth all generations will call me blessed", as proof that she is a figure fit for veneration, so whatever Jesus replies with makes or breaks their entire case. As it turns out, Jesus' response breaks the case from Luke 1:48. In Luke 11:28, Jesus replies with "more than that, blessed are those who hear the word of God and keep it!"
In other words, as great a blessing as Mary received by being the one woman, out of millions, whom God chose to bear the Messiah, that blessing does not compare with hearing and keeping the word of God. Mary herself could increase her blessing by obeying God! Mary isn't to be venerated, she follows the same pattern as all human beings.
A final thing worth noting is that Jesus is one of the few people ever to walk the earth who genuinely was morally required to honour Mary. This is because, as her Son, Jesus had to honour His mother and father, keeping in step with the 5th commandment. Thus, since the only person ever to walk the earth without sin, who demonstrably was required to honour Mary, did not honour Mary in the manner Catholics do, Catholics simply have no case.
So, to recap, there are no Biblical commands to "venerate" Mary, there are Biblical commands against venerating Mary, particularly as "Queen of Heaven", and against even attempting to talk to her. Aside from all this, we have Jesus' own example, as He even blanked Mary sometimes. The blasphemous view Catholicism preaches about Mary is all the proof any sane observer should ever need to know that Catholicism is a toxic milkshake of Christianity and a host of pagan religions it has absorbed like a sponge over the centuries. The correct was to honor Mary is to honor her son, the Son of God, whom even she acknowledged as her saviour.