Bring water to a boil in a pot; add chicken bouillon and stir until dissolved.

Drain and rinse 1 can Great Northern beans. Reduce heat to low; stir drained beans and remaining can of undrained beans into bouillon mixture. Add carrots, onion, celery, garlic, bay leaf, and black pepper; bring soup to a boil.

Stir ham into soup, reduce heat to low, and simmer until vegetables are tender, about 30 minutes. Season with salt.