I usually save the bag to put the wrap, fat and other trimmings into and tie it up before it goes into the trash. Sometimes, I'll put them in the bag, then in a used ziplock.
Those same types of bags are used by athletic trainers to put ice into. Why, I don't know, because they always leak.
I usually put my meat scraps, etc. into a used plastic bag and put them into the freezer and then put them in the trash the night before or the morning of trash pickup to keep them from stinking up the place. Nothing worse than rotting chicken guts.