Cover chicken with water, and bring to a boil in a large Dutch oven. Add 1 1/2 teaspoons salt, 1/2 teaspoon pepper, and next 3 ingredients; cover, reduce heat, and simmer 1 hour. Remove chicken, reserving broth in Dutch oven; cool chicken. Skim fat from broth; bring to a simmer.
Skin, bone, and coarsely chop chicken. Add chicken, bouillon, and remaining salt and pepper to broth. Return to simmer.
Combine flour and poultry seasoning in a bowl. Cut in shortening and bacon drippings with a pastry blender until mixture is crumbly. Add milk, stirring until dry ingredients are moistened.
Turn dough out onto a lightly floured surface. Roll out to 1/8-inch thickness; cut into 1-inch pieces.
Bring broth mixture to a boil. Drop dumplings, a few at a time, into boiling broth, stirring gently. Reduce heat, cover, and simmer, stirring often, for 25 minutes.