In my kitchen, I have a Simple Human trash can. I also purchased their Compost Caddy that clips to the side of the trash can. When I purchased the caddy, it came with these bags. I've never had an issue with them breaking down. My compost is in a plastic trash can in my backyard, so I wouldn't consider it a hot pile. Been using them for two years, it takes longer than other materials, but it does break down.

Just make sure you dump out the contents of the bag into your Tumbler and then just throw the bag in there. Don't let the material sit in the bag inside the tumbler.