Yup. I always carried or wore a bandanna anyway, but since March I've tucked a surgical mask and latex gloves in a small ziplock baggie into my jersey pocket every ride.
I've worn it whenever I need to stop in a convenience store -- only three times since March because I usually carry enough water and snacks to avoid needing to stop. I'll probably stop more often in summer because it's harder to carry enough water to last more than 30-40 miles.
I rotate among three masks for awhile before discarding them and getting new ones -- I already had a box full of masks, gloves, etc, before the pandemic.
I use a fabric steamer - the kind designed to de-wrinkle delicate clothing -- to disinfect and freshen up the surgical masks. Those blue surgical masks are both tough and delicate. They'll last many reuses with care, but the outer mesh poly fabric melts easily from direct heat such as from a low iron. But no problems using a fabric steamer, which gets scalding hot.
I worked in health care for years and had to wear masks for hours at a time, and respirators with filter canisters as a safety and health inspector. Not a problem, even with my asthma and allergies. You get used to the slight stuffy sensation. The main challenge is heat buildup. Often I'll wear Breathe Right or similar strips over the bridge of the nose, or Rhinomed Turbine inserts, to keep my nasal passages open -- I have a deviated septum from boxing so occasionally it gets congested. With a good inhaler from my allergist and the mechanical nasal doodads I can usually avoid needing Sudafed or ephedrine.