What was Moses doing when he came to the burning bush?

Answer: Shepherding a flock

Moses was leading his father-in-law's flock to the far side of the wilderness when he saw the bush ablaze.

“Meanwhile, Moses was shepherding the flock of his father-in-law Jethro, the priest of Midian. He led the flock to the far side of the wilderness and came to Horeb, the mountain of God. There the angel of the LORD appeared to him in a blazing fire from within a bush. Moses saw the bush ablaze with fire, but it was not consumed.”— Exodus 3:1-2 (BSB)