I got a BOCO mask that I keep in a jersey pocket. The main criterion for me was that it’s made of non-absorbent tech fabric (polyester) so it still works well if a bit damp (unlike the cotton masks we use for day-to-day). De Soto, Wattie, etc. would probably also work.
For running, I’ve seen folks wear it on their wrist like a bracelet. Personally, I try to avoid situations where I’ll need it and just have it in case I need to assist another cyclist with a flat/mechanical, or if I bonk and need to go into Robert’s.
https://www.amazon.com/...597962197&sr=8-2
https://www.bocogear.com/...category/face-masks/
Thanks Titanflexr! - I got one of those kinds of masks; very handy and easy to use though I don’t think they provide much protection. But will probably be my go-to for riding and running.