Combine first 4 ingredients in a large Dutch oven. Bring to a boil. Reduce heat; cover and simmer 30 minutes. Add collard greens and beans; cover and simmer 30 minutes.
Sauté onion and green pepper in drippings until tender. Add sautéed vegetables, potatoes, salt, and pepper to collard green mixture; stir well. Cover; simmer 30 minutes or until vegetables are tender. Remove and discard ham bone and salt pork.
Spoon soup into individual bowls. Serve hot with cornbread, if desired.