Perhaps that isn't a problem later on, but at this point in our breastfeeding adventure, I let down like a garden hose on full blast, and the Baby Beast usually lets go (to prevent drowning; obviously, he's smarter than his blank expression lets on) which means the bed takes the brunt of the spray (yes, we have mastered side-lying nursing).
So, I figured the best thing I could do is either put a raincoat underneath both me and the baby (which seemed like a very crinkly, plastic-y idea) or layer the bed underneath the baby with receiving blankets and prefold cloth diapers. You can guess which one I chose.
Obviously not a raincoat
Luckily, these absorb the brunt of the blast, and I change them every evening before we crawl into bed.
So, if you're planning on co-sleeping and breastfeeding, be aware that someday a raincoat (or some prefolds) might save your sheets.