Inhaling bleach can be harmful especially in large amounts and you should always open windows if possible to allow fresh air into the area so that you don't breathe in the bleach fumes and become sick.
Breathing in too much bleach fumes without getting fresh air can severely harm the tissues of your breathing system.
The bleach fumes could also kill you eventually if you don't get out into some fresh air.
The bleach fumes can also cause other respiratory issues and breathing problems in the future.
I never clean with bleach unless I can have windows open to allow fresh air in because I really start coughing when the fumes of bleach are in the air but I don't feel the effects with the windows open though.