I have a thing called a Hayzee which works ok. I fold a towel up and put it in a pillowcase and line it with that. I can’t use loose bedding, was not willing to use extremely un-environmentally friendly puppy pads and found that when using a little 1x2 fleece cage liner all of the hay would stick to the fleece.
I bought towels and pillowcases from charity shops and use those, I think it works quite well as they can be separated for washing, can be washed at higher temperatures than fleece, can be tumble dried and the hay only comes into contact with the outside of the pillowcase which can be turned inside out so all of the leftover hay/hair gets caught in the corners and can be removed in a clump after drying.