Can I use 100% cotton bed linen as a pudding cloth?
If you wash them first, there's no reason you can't.  Muslin is just fabric.  It doesn't even necessarily need to be undyed (although it can matter what color the dye is), and doesn't necessarily have to be cotton (although some synthetics won't pass enough moisture).

It's fairly traditional for cooks to use an old pillowcase for boiled puddings.  According to a Regency Fiction blog, most 19th-century pudding cloths were linen bedsheet remnants.