Bamboo is a sustainable fiber, and does not depend on oil as most synthetic fibers do. Mattresses that use natural bamboo fiber covers include Englander and Symbol, but there may be more. Simply check out the cover material as opposed to the materials used in the interior layers of the mattress that wrap the spring unit.
Well designed mattresses can solve these problems, whether they are of the pocketed spring or innerspring design. You never sleep on top of the springs themselves, but on layers of foam between your body and the springs. These layers are chosen for their particularly properties, and the more you pay for your mattress, then the more comfortable and supporting these layers should be.