Only dog poop bags that are labelled as biodegradable- not degradable- will break down into eco-friendly waste such as water or biomass which can be consumed by natural matter. The Federal Trade Commission (FTC) say that companies who claim their bags are biodegradable should clearly state the length of time that it’s expected the bag will take to naturally decompose.
You should also be aware that throwing your dog poop bags in with your general waste means that your bags are more likely to end up in landfill, where it will take considerably longer for your bags to degrade.