There are many ways to make a box for dispensing plastic bags for picking up dog waste. Below are ideas for making boxes for dispensing bags.
This box is made by SImply Human and was purchased at Target for $10 (though Target no longer carries it, you can purchase it online.) It was designed to hold plastic grocery bags. We turned it upside down and painted it with primer and then with outdoor paint. We then sealed it with a spray clear coat varnish. It comes with holes in the back that are perfect for mounting with bolts, ring washers, and nuts. The oldest Mess Mitt Box in the Neighborhood is about 3 years old and still holding up well. Speaking from personal experience, we find that the long orange and green bags that newspapers come in make excellent dog poop dispensing bags.