Perhaps you've seen the Sun Chips commercials that show the bag breaking down in the soil. It seems like a cool idea, right? We all use plastic bags, so if we can manufacture biodegradable ones, it seems like our problems are solved.
The science says it doesn't really work. There are several problems with the biodegradation process for plastic bags. First, there are many environments in which little to no degradation takes place, such as in landfills, in low temperatures, and in humid evironments. That pretty much cuts out the process of degradation in most of the possible contexts.
Secondly, the bags still take a lot of oil to manufacture. It's still a waste of resources, whereas reusable bags utilize the least amount of energy, given that you can use them over and over. It's still possible to recycle biodegrable bags, but once they have the stamp of biodegradability, how many people do you think are really going to be induced to do that?
Thirdly, there is a question of how toxic the biodegraded remnants are. Many of the ingredients added to help the degradation process are harmful, and remain in the environment after the bag has broken down, including lead and cobalt.
So, stick with your best choice: reusable bags. And if you end up with a plastic bag here and there, please recycle them.