Note that there are two kinds of "biodegradable" plastics. Vegetable based plastics (which are definitely unproblematic when left in the environment) and "OXO-biodegradable" plastics which are just normal plastics (like PE, PP, PS) with additions that make them break down quicker than normally. If a bag feels like a normal plastic bag then it will be one of the latter kind; vegetable based plastics have a different feel to them (kind of rubbery), to my understanding; since they are produced in a different way (by a different industry), and more expensive, you rarely encounter them.

The Wikipedia article on OXO biodegradable plastics[1] seems to be heavily edited by industry participants. Last I heard[2] was that OXO-biodegradable plastics are basically cheating, as they leave the plastic in the wild, just invisibly (perhaps even making things worse as then it can't be collected anymore?). The Wikipedia article argues that the fragments will be decomposed by organisms. I don't know which is true, but wanted to point out that there are two kinds and you should be careful not to mix them up in discussions.

    [1] https://en.wikipedia.org/wiki/Oxo_Biodegradable
    [2] from the film Addicted To Plastic [3] 
        or other places, not sure anymore
    [3] http://www.crypticmoth.com/plastic.php

But then we might have to spend money on things that last longer :/