I get the big rectangular bales that weigh about half a tonne.
I have a house cow so the straw goes down as bedding. She eats quite a lot of it too but it ends up as cow muck that gets deposited onto the bedding straw. It all gets forked up and goes in our compost bins.
I put a thick layer of straw on the top of my compost heaps to keep the heat in and exclude light from the top so the worms come up further. I just lift it off and spread it on the next heap when I turn a heap.