Prior to the burning bush event - what was Moses's knowledge of God? We know that he went to live with the Egyptians from a young age to the age of more or less 40. He then lived in Midean for another 40. It seems that there was no contact with other Israelites. Or was there a role played by his father in law?
There is only speculation as to who told moses what, and when. The bible doesn't say whether there was any contact between moses and his biological family after he was weaned and taken back to Pharoah's daughter (until he was joined by his brother Aaron and his sister Miriam in Egypt, when he went to face the Pharoah). He did know that the Israelite slaves were his brethren; but who told him? Pharoah's daughter knew Moses' sister, Miriam, and possibly her mother. One of them could have visited him and told him his family history and of God. 

Jethro was the priest of the Midianites. Midian was one of Abraham's six sons by Keturah, whom he married after Sarah died. Jethro was most likely a priest of the God of Abraham, being one of his direct descendants. It is very likely that Jethro told him about Abraham, Isaac, Jacob and their God, when he lived with him for 40 years.