The early religion of the Canaanites and the Israelites were closely related (See See Daniel C. Peterson, . "Nephi and his Asherah." Maxwell Institute. Maxwell Institute, n.d. Web. 29 Jun 2012.). In the Canaanite pantheon the chief deity was El, whose wife was a goddess named Asherah (aka Elat - the feminine form of El). Additionally, as Daniel Peterson explains:
"In the earliest Israelite conception, father El had a divine son named Jehovah or Yahweh.4 Gradually, however, the Israelite conception of Yahweh absorbed the functions of El and, by the 10th century BC, King Solomon's day, had come to be identified with him.5" (Peterson, "Nephi and his Asherah").
Asherah (אשרה) was commonly associated with many different types of trees including the almond tree. She was also associated with the concepts of fruitfulness, posterity, fertility etc. One of the main features in the temple at Jerusalem was the menorah which represented a stylized almond tree (see Exodus 25:31-35). Therefore, in the minds of the Israelites the menorah was probably connected with Asherah. It is interesting to note also that the burning bush and the menorah were both, in essence, burning trees and the Israelites would have undoubtedly have seen this connection as well.
Additionally, rabbinic writings associate the burning bush with the Shekinah or Divine Presence. The word Shekinah is a feminine word (the -ah ending making it feminine) and was thought of as having feminine attributes (See Louis Ginzberg, "Legends of the Jews.", http://philologos.org, Web 30 Jun 2012.).
We see, therefore, a strong connection between Asherah and everything associated with her and the burning bush. That connection is reinforced by the text of Exodus itself and the account of the interaction between Moses and God.
In Exodus 3, verses 2 - 6 describe how Moses sees the bush from afar, draws closer to investigate, is told to remove his shoes and then speaks with the Lord. The Lord then identifies himself to Moses as the God worshipped by Abraham, Isaac and Jacob, but does not use the name יהוה (Jehovah or Yahweh).
However, later in Exodus chapter 6 verses 2 - 3 the Lord explains that:
"I am Jehovah. And I appeared to Abraham, to Isaac and to Jacob, as El Shaddai, but by my name Jehovah I did not make myself known unto them."
In the King James Version (KJV) of the Bible El Shaddai (אֵל שַׁדַּי ) is usually translated as "God Almighty". As has been discussed in other posts, the name/title of El Shaddai carries a female connotation which is generally used while discussing the concepts of fertility, posterity, fruitfulness etc. (See Gen. 28:3 for example).
The Israelites were on the cusp of being delivered from bondage in Egypt and coming into being, as a distinct nation. It would appear, therefore, that God, by appearing in the burning bush, was sending a clear message to Moses and the Israelites that they were about to be delivered (or born) to a fruitful land to be made a fruitful people.
