Man Sewing YouTube Video
https://www.youtube.com/watch?v=V0e3ZN3gfFg He is making a dog bed for a smaller dog, but it would not be hard to make it larger.
To handle incontinence, I would make the tube and top layer of the bed out of PUL, the fabric diaper covers are made out of. Them make several small pads that can go inside for your old gal. You would just have to wash the pads.
For stuffing I would not use cotton fabric scraps, if you ever had to wash the bed it would take forever to dry. I would use fleece scraps, poly batting scraps, but mostly pillow stuffing.