The theme of Our Lady depicted as the burning bush was also seen in one of the icons from the Sinai exhibit and is one of her ancient titles. She is the holy ground where God, the "I Am Who Am", is present. She is this burning place of God's visit that doesn't consume her.
Our Lady, when asked by St. Bernadette, gave her name as: "I am the Immaculate Conception." She is who God made her, wholly consecrated to him from the beginning to bring Christ to the world.
Another famous painting with this theme is explained by Rev. Theodore A. Koehler, S.M.
[I]n a very sophisticated masterpiece ["The Burning Bush"], Nicolas Froment (1475-1476) represents the biblical scene in which Moses, pasturing his sheep, was surprised to see a bush in flames and not consumed. The painter represents Moses and his sheep with the angel speaking to Moses, in the inferior part of this painting. In the center of the upper part, various rose trees merge their leaves and flowers into a great burning rosebush; in the midst, Mary is sitting with the Child Jesus. The symbolism of the Rose is enriched with the symbolic meaning attributed to the burning bush since Gregory of Nyssa: a figure of the virginal conception and birth of Christ.