I think it spreads because people think it is another person. They approach, they are grabbed by the zombie, then bitten. It's pretty simple logic. Anybody who sees it will run away and pretend it has never happened and the brave people who try to kill them will eventually die. The government gets wind of it and they try to keep everyone under control, grouping them in places etc. One zombie gets in and that's it everybody is zombified or dead. Anybody who is smart or lucky will runaway from that area or never be there in the first place.