Bugs such as campylobacter can be found on the outside of up to 4% of poultry packaging and this could be transferred onto the material of the bag. If you later use the same bag for items that do not require cooking, e.g. salad vegetables, then they could pick up those germs from the bag.
Keeping a separate bag for life that is only used for raw meat and nothing else may be one solution.
Stores such as Morrisons also intermittently sell fabric reusable bags that can be put through the washing machine, as and when required.