Why did Moses' hair became white when he saw the burning bush?

It didn't.

During the encounter with the 'burning bush', The Bible does not say that Moses' hair turned white....but his HAND did. When he saw the 'burning bush', he 'concealed his face', but nothing is mentioned about his hair.(Exodus 3:1-6). As God spoke to Moses, explaining what was expected of him in Egypt, he demonstrated his power by turning Moses' hand 'white as snow' with leprosy, and then healing it again(Exodus 4:6-7).

Later, when Moses received the 'two tablets' with the ten commandments on them from God, his 'face emitted rays'(Exodus 34:29+30), but, again, nothing is mentioned about his 'hair turning white'. Only in the movie is this indicated, probably to make the point about the 'rays' lighting him up, but that's more 'artistic license' than factual.