How to treat burning eyes caused by the fumes from bleach?

Lubricating drops. The eyes are very sensiive to bleach fumes and will water excessively when exposed which gets rid of most of the bleach. If you vision is clear, the eyes are not particularly red and there is no pain, you can just use over the counter lubricating eye drops to help flush out the rest. If there is any problem, see your ophthalmologist.