How do you dispose of the trash after using a modeling pack?

Applying a modeling pack is a hassle, but it's really inconvenient to throw away the shell shaped like my face that comes out afterward.

If you put this in the trash can without drying it, mold grows on it.

I'm curious how everyone else handles the disposal. I'd like to do it often, but it takes time to dry and throw these things away... ㅠㅠ And I can't just leave them hanging everywhere either.