PLA starch bags
PLA plastic is made from plant-based materials such as corn starch. You can find about more about starch derived plastics here .
Once again they are compostable and certified as such.
One example of PLA bags is sold by the company Biobags. Back in the early days they were amongst the first to sell in the U.K. They have very good credentials. Their bags are certified to BS N13432 standard and are manufactured sustainably at facilities certified to ISO 9001 and ISO 14001. BioBag is the world’s largest brand of certified biodegradable and compostable bags and films made from Mater-Bi®. Biobags are the bags used in Modbury the plastic free town.
What is compostable? To be classed compostable, items must biodegrade within a certain time (around the rate at which paper biodegrades), and the resulting biomass must be free of toxins, able to sustain plant life and be used as an organic fertilizer or soil additive. For a man-made product to be sold as compostable, it has to meet certain standards. One such is the European Norm EN13432. You can find out more here.