Bleach consists of sodium hypochlorite, hydrogen peroxide and other chemical substance. All these substance are oxydic. When bleach comes into people's eye, it will react there and oxidizing reaction will release heat so that you will feel burning in your eyes. You should rinse your eyes will code clean water immediately. Oxide will be less sensitive at lower temperature and the running water will take away the heats, so that the burning will be partly relieved. And then, use antibiotic eye-drops as it is helpful to stop oxidizing reaction. At last, put on the ointment to help the eyes recover. If it doesn't work even you have done all these job, you have to go to see a doctor.
It will make your eyes burned and let you feel painful. So do something as soon as possible. The first thing you should do is not washing your eyes in the water. Just be careful about the water which will just make the situation more and more serious, because, the bleach is a kind of chemical that can be active in water. Then, you are not supposed to do something by yourself and just clean your eyes with a dry cloth. Then, go to the hospital as soon as possible so that the doctor can help you.
That is awful! Immediately, wash your eyes with lots lots of water till you feel better.
If your vision is clear, your eyes are not red and painful, you can use over-the-counter eye drops to heal your eyes. Otherwise, consult your ophthalmologist.
In the end, I advise you to find out where the bleach comes from. And do not let it into your eyes anyway.