Are blue rosary beads based on blue ribband (tzitzit) from Numbers 15?
The short answer is no.
Blue is simply a Marian colour.
The colour blue is simply the traditional colour of the Virgin Mary from about the the year 500 on.
For example the colour blue in Mary’s mantle seems to have originated around the year 500 AD and is of Byzantine origin. Most sources seem to point to this date as the Byzantine origin of the color blue of Mary's mantle.
Why Does the Blessed Virgin Mary Wear Blue?
In many artistic portraits of the Blessed Virgin Mary, she is depicted wearing a blue mantle. Why blue?
In first century Galilee, Mary’s clothing would probably not have much color. It would have been more flaxen-wool colored. Villagers may have used available plants to produce some modest dyes. Purple and blue were reserved for the rich and ruling classes because plants for those dyes were more rare. Red was used for the Roman army because plants producing red dyes were readily available.
As Mary has appeared throughout the centuries, she has worn different colors and styles of clothing.
•Our Lady of Fatima (1917) appeared to the children wearing a gown and mantle of white with gold trim and a crown.
•Our Lady of Lourdes (1858) appeared to Bernadette wearing a simple gown and mantle of white with a blue sash.
•Our Lady of Guadalupe (1531) appeared to Juan Diego wearing a gown of rose and a mantle of blue with gold stars.
Fr Johann Roten SM, director of the Marian Library-International Marian Research Institute at the University of Dayton (a Catholic college) wrote: “Mary’s dark blue mantle, from about 500 AD is of Byzantine origin and is the color of an empress.”
Blue has been a color associated with royalty, peace, and nature (sea and sky). So it makes sense that artistic renditions of Mary portray the Queen of Heaven and Earth in blue.