This can be a funny question, but it is asked a lot. Yes, you can kill termites with bleach. Bleach will kill termites instantly, but it you will not be able to eliminate the bigger problem. You can kill the termites that you see, but you can't get a hold of the entire colony with bleach. They breed and spread out fast.
If you have formosan or subterranean termites, you can't access the colony or the queens at all. Not only that, they are very fast at destroying your home. So does bleach kill termites? yes, but not recommended. Call a professional and save your house.
Bleach as Termiticide
Another reason why you shouldn't use bleach as termiticide is because bleach is extremely dangerous to plant life. Bleach can generate toxins like dioxin to soil. When it happens, you will have no luck growing plants on that soil. Also, bleach can contaminate water source or water table.
Some people think bleach is organic because it comes from table salt. But it's not organic. Bleach is created by spliting table salt into chlorine and caustic soda. As you may know, both chlorine and caustic soda are very dangerous substances. Bleach reacts with common household chemicals like ammonia and vinegar to produce deadly toxic gases. Not only that, it smells awful.
Chlorine Contaminated Soil
Chlorine, the main ingredient of bleach, is extremely harmful to soil's health. If you apply bleach on soil to kill termites, you will end up killing all living organisms including earth worms. Once chlorine is spread out with rain, it will kill one plant at a time. It is just an awful way to kill ants and termites. Just don't do it. Here is a screen shot of a forum post to show you what chlorine can do to your soil.