Mine stays on the bike handlebars. I wash it and hang it there to dry. I put it on with the helmet, but most of the time it is around my neck. Only pulling it up when I am near others, or riding with a group. I also take wet wipes with me to make sure my hands stay clean and germ free.
I would like to stay free of this crud, had pneumonia once and it took 4 months to get back to where I could bike again, and that was an early catch, and antibiotics. So within a week it was on its way out, just the lungs had to heal, takes a long time. It sucked.