Tie the celery, carrot, thyme, parsley, and bay leaf into a bundle using cotton butcher's twine. Place the beans, bundle, and onion into a large pot. Add just enough water to barely cover the beans. Bring to a simmer, partially cover, and cook until beans are barely tender, 1 to 2 hours. After 30 minutes, add the salt to the beans. Occasionally check on the beans and add water to cover the beans, if needed.