The burning bush is a picture of God's grace. Brown-Driver-Briggs' Hebrew Definitions says the bush is a thorny bush which reminds us of the curse (Gen. 3:17-18), i.e. original sin. God is described as a "consuming fire" (Deut. 4:24, 9:3; Heb. 12:29), and fire is also typical of God's judgment (2 Pet. 3:7). So the burning bush is sin being judged but not consumed. It speaks of God's grace. We deserve to be judged for our sin and to be cast into eternal punishment. But God in His mercy sent His only begotten Son, Jesus Christ, to be the perfect sacrifice for sin and to become our substitute.
"But he was wounded for our transgressions, he was bruised for our iniquities: the chastisement of our peace was upon him; and with his stripes we are healed. All we like sheep have gone astray; we have turned every one to his own way; and the LORD hath laid on him the iniquity of us all...Yet it pleased the LORD to bruise him; he hath put him to grief: when thou shalt make his soul an offering for sin, he shall see his seed, he shall prolong his days, and the pleasure of the LORD shall prosper in his hand. He shall see of the travail of his soul, and shall be satisfied: by his knowledge shall my righteous servant justify many; for he shall bear their iniquities." (Isaiah 53:5-6, 10-11)
Remember Jesus said, "If I be lifted up, I will draw all men unto Me." (John 12:32) And this is what happened. Moses essentially was attracted by the cross. ["By faith Moses, when he was come to years, refused to be called the son of Pharaoh's daughter; Choosing rather to suffer affliction with the people of God, than to enjoy the pleasures of sin for a season; Esteeming the reproach of Christ greater riches than the treasures in Egypt: for he had respect unto the recompence of the reward." (Hebrews 11:24-26)] He was drawn by God's grace, and then God called Him. In other words, the only hope for humanity is Jesus Christ and Him crucified. It is the only thing between us and eternal perdition. But praise God for His amazing grace!
For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life. (John 3:16)