What happens if you burn yourself with hair bleach?

I'm not entirely sure what you mean by burning yourself. If you mean the burning sensation you feel on your scalp when you've applied bleach to your roots, then that means you applied the bleach to your roots too soon or you left it on to long.

Every at home bleach kit comes with instructions for a specific reason; bleaching hair is severely damaging and can be (if not done properly) somewhat hazardous for your health.

How lightening or bleaching works is it opens the pores of your hair shaft and breaks down and decomposes the melanin(color) of the hair. During the process it diminishes strength and the chemical bonds in your hair, which is why when some people bleach their hair it falls out. Bleach should have minimal to no contact with skin because it can be absorbed by your skin just like it can be absorbed by your hair and unlike your hair, your skin will become irritated and more than likely bleed.

If you did happen to damage your scalp while bleaching, my suggestion to you is to gently rinse your scalp with room temperature water and don't rub or scratch, that will make it worse and could cause infection. Blot your head dry and avoid using heat. If you were bleaching your hair to radically change your hair color and your scalp was damaged, I strongly suggest waiting 24 to 48 hours before you complete your hair project, for the sake of your skin's health.

The next time you decide to bleach your hair, please read the included instructions thoroughly and follow them precisely. I also think consulting a professional to learn more about your hair's texture, courseness and porosity to help you determine how long you should leave the bleach in your hair and when you should add bleach to your roots.