Do you have to insure your bike in Japan? And if so, how?

It is not necessary to insure your bike in Japan. However, it might be a smart thing to do. In 2013 a mother had to pay 95 million, because her son had struck and elder woman who ended up being in a coma.
What you do need to do is register your bike with your name at the prefectural police department. This way the police will know that your bike is actually yours when they are doing controls or when your bike is stolen. Registration costs 500 yen and will be done when you purchase your bike at the shop. Don't forget to bring your ID.

You should definitely register it Jason!
Many times the police has stopped to check my bike and I think they might have taken it away if it was not registered in my name.

Hahaha yes I heard that the most stolen things in Japan are actually bikes and umbrellas! I guess umbrellas because when you enter a store you have to leave it in an umbrella basket before you enter the store and since many umbrellas in Japan are either made out of clear plastic or black material, so its easy to pick up the wrong one when you leave the store. So I guess it doesn't really happen on purpose. For the bike I guess it's a matter of always locking your bike.