There is loads of choice out there - just google dust masks, anti microbial masks, anti allergy masks or similar and you will see a huge variety including both hard and soft masks. The problem I had with the lovely soft anti microbial mould and dust masks I bought at the start of the H1N1 flu scare, was that I couldn't cope with wearing them for more than a minute at a time. After a while I binned them. I couldn't stand the feeling of suffocation.
My only solution for household dust has been to either 'damp dust' or buy those micro fibre dusters from the supermarket that claim to 'pick the dust up rather than just moving it around'. I have a couple of washable fabric ones, and a pack of disposable ones. I also use medical grade clinell universal sanitising wipes on household surfaces once a week. I don't sweep the kitchen floor anymore but hoover it instead. The biggest problem is cleaning the bathroom as I can't stand fumes from cleaning products. I use Ecover products for most things now, though when I can no longer resist the urge to bleach the Loo, I open the window , throw some down the Loo then leave quickly closing the door behind me. Some time later I return gulping enough air in to fill my lungs, hold my breath, attack Loo with brush, flush, and beat a hasty retreat back out of the bathroom - and yes - i look very silly doing these things