Do you put those items in the same bin as the plastic bags (at the grocery store)? I ask because I regularly take my plastic bags to that bin and I have NEVER seen anything other than plastic bags. I've been wondering where to put those white amazon packaging for "Store Drop Off" but I don't see where other people put them.
bubble wraps covered by paper can be soaked in water to separate the paper and then reuse or recycle the plastic layer. The plastic is the headache to begin with so try to recycle as much