Yes, we Catholics have a whole month devoted to Mary. Not devoted to worshiping her, but devoted to seeking her intercession and learning how to be more like her. We entrust ourselves to her care. Why? Many reasons, but to put it simply: because God entrusted Himself to her. This woman was pure and sinless, a humble Jewish woman who trusted God with her whole life, body and soul. She carried the Son of God inside herself, gave birth to Him, raised Him. Then she felt a sword pierce her immaculate heart as she watched her perfect, sinless boy suffer under the crushing weight of our sins. While He was on the cross, He offered her to us: "Behold, your mother." (John 19:27) He gives her to his beloved disciple (HINT: that's YOU). We would be fools not to accept her motherly love and guidance. After all, if we want to be like Jesus, shouldn't we entrust ourselves to the same motherly love and guidance He had while on earth? I mean, I think so.
If you aren't convinced (okay, even if you are), check out Father Michael Gaitley, MIC's 33 Days to Morning Glory: A Do-It-Yourself Retreat in Preparation for Marian Consecration. The book contains thoughts and reflections of Mary by Saints Louis de Montfort, John Paul II, and Maximilian Kolbe as well as Blessed Mother Teresa. Insightful and inspiring, it's a great explanation of how Mary helps us grow closer to her Son.
If you're looking for a shorter, simpler way to grow closer to Mary, try the 31 Days of Mary. I don't remember how or when or where, but at some point while I was at school, I stumbled on this gem of a devotion for the month of Mary. For each day of the month of May, there is a virtue of Mary and a little blurb for reflection. It's a simple way to meditate on Mary each day during the month we devote to her. I've searched online and can't find the source of this simple prayer, so, hoping that I'm not infringing on anyone's rights, I typed it up, made a few adjustments, and posted it on this blog in the right hand column under "Pages."
May it bring you closer to Our Lady and Our Lord!