Closing off HVAC vent plus washing it with bleach

One of these mornings I am going to kill myself cleaning the tub. I hate when mold forms around the drain plus corners of the tub. I hate the soap scum on the sides plus the dirt welded to the floor of it. I then have enough of it plus get out our tools. I have bleach plus tons of cleaners that all contain some portion of bleach. I have a heavy duty clean brush plus towels to mop up our work. I don’t want the bleach to get into our indoor air pollen levels plus make the whole home reek; So what I do is close the air vent in the bathroom. The smell then stays in the area. I close the door so no smells will leak out that way either. Without heating or cooling flowing in the space, the smell just says in the bathroom. I have gotten now where I open the small window in the bathroom to allow natural ventilation in there. Even with this, the bleach smell is super strong. I always suppose I am going to die since the bleach gets myself and others coughing plus our eyes watering. I get where I can barely breathe plus see the air quality is so contaimied. Every now plus then every one of us will stick our head out the window to get fresh air. If I let the Heating plus A/C into the space, it would not be so bad, and but then the smell would be all over the arena. I am willing to take a little coughing to keep the rest of the household safe.
Cooling tech