Hi, Michael —

Thanks for the question.

She become associated with roses through events that happened in the twelfth century.

It was in the year 1214 that the Church received the Rosary in its present form and according to the method we use today. It was given to the Church by St. Dominic, who had received it from the Blessed Virgin as a means of converting the Albigensians and other sinners. Saint Dominic, seeing that the gravity of people's sins was hindering the conversion of the Albigensians, withdrew into a forest near Toulouse, where he prayed continuously for three days and three nights. During this time he did nothing but weep and did harsh penances in order to appease the anger of God.

At this point our Lady appeared to him, accompanied by three angels, and she said,

"Dear Dominic, do you know which weapon the Blessed Trinity wants to use to reform the world?"

"Oh, my Lady," answered Saint Dominic, "you know far better than I do, because next to your Son Jesus Christ you have always been the chief instrument of our salvation."

Then Our Lady replied,

"I want you to know that, in this kind of warfare, the principal weapon has always been the Angelic Psalter [Rosary], which is the foundation-stone of the
New Testament.

Therefore, if you want to reach these hardened souls and win them over to God, preach my Psalter."

So he arose, comforted, and burning with zeal for the conversion of the people in that district,
made a path straight for the cathedral. At once unseen angels rang the bells to gather the people together, and Saint Dominic began to preach.

The following was taken from the New Advent web site.

It is certain that in the course of the twelfth century and before the birth of
St. Dominic, the practice of reciting 50 or 150 Ave Marias had become generally familiar.

As regards the origin of the name, Rosary, the word rosarius means a garland or bouquet of roses, and it was not infrequently used in a figurative sense —
e.g. as the title of a book, to denote an anthology or collection of extracts.

An early legend which after traveling all over Europe penetrated even to Abyssinia connected this name with a story of Our Lady, who was seen to take rosebuds from the lips of a young monk when he was reciting Hail Mary's and to weave them into a garland which she placed upon her head. A German metrical version of this story is still extant dating from the thirteenth century. The name "Our Lady's Psalter" can also be traced back to the same period. Corona or chaplet suggests the same idea as rosarium. The old English name found in Chaucer and elsewhere was a
"pair of beads", in which the word bead originally meant prayers.

It should also be noted that Our Lady has appeared with roses in many approved and unapproved apparitions of her.

Hope this answers your question.

Mike