Used chicken coop bedding is nearly perfect for rapid breakdown.
Compost bins are for pretty. Stuff composts just as well in a well-built pile.
You need to stack it by laying down 4-6 inches, moistening it so that its like a wrung-out sponge, laying down another 4-6 inches, moistening it, ... until you have a cubical pile at least 2-3 feet wide and at least 2-3 feet high. (4x4x4 being close to ideal, or, if you have more, extend the width to make it 4x8x8).
If it wants to pack in a way that excludes air or if you have a very wet climate, use long straw, corn stalks, or brushwood to make a chimney in the middle and a few air vents in between the layers.
If you have a very wet climate you should round off the top to prevent it from absorbing too much water. If you have a dry climate, dish the top to make sure you collect precious rain.
You can just leave it as is and it will break down in 6 weeks to 6 months depending on climate and season.
Or you can turn it a couple times each week, so that the outside material is moved to the inside and the top to the bottom and you'll get compost in about a month in any climate (may need to tarp it against excess rain and/or insulate it against freezing solid.
IMO, intensive turning is too much work. Compost happens by itself if you build the pile even close to right.