You could use a mask pouch, personally I just stuff them back in the bags the mask came in.
Forgot to mention, masks filter through 3 main principles: static electricity to attract particles, Brownian motion (basically stuff in the air zigzags around which increases the likelihood it ends up caught in a filter when the particle is smaller than the filter size), and the filters themselves.
For example, if a mask filter size was 3nm, that is the size it is *least* capable of catching (so n95 95% rating comes from this), whereas particles above and below this size are more effectively caught due to above-mentioned concepts. The most likely part of the mask to degrade with usage will be the static electricity part, due to moisture in your breath getting the mask all wet (so valved masks would be better if you don't care about helping your fellow non-masked passengers). However, that is offset somewhat because a mask's filter efficacy does go up the more clogged up with stuff it gets too.