Melt butter in a large saucepan over medium heat. Cook onion in butter until translucent. Stir in flour until smooth, then gradually stir in 2 cups water, carrots, celery, garlic, salt, and pepper. Heat through, then stir in milk. Dissolve chicken base in 1 cup warm water, and pour into vegetable mixture.
Place potatoes in slow cooker, and pour heated vegetable mixture into potatoes. Place bay leaf in pot.
Cover, and cook 5 hours on High, or 8 hours on Low.
Remove bay leaf. Puree about 4 cups of the soup in a blender or food processor, and then stir pureed soup into contents of slow cooker. Stir in cheese and bacon until cheese is melted.