Whose bones did Moses take with him out of Egypt?

Answer: Joseph's

Moses took Joseph's bones, because Joseph had made Israel swear to carry his bones up from Egypt when God came to their aid.

“Moses took the bones of Joseph with him because Joseph had made the sons of Israel swear a solemn oath when he said, “God will surely attend to you, and then you must carry my bones with you from this place.””— Exodus 13:19 (BSB)