Melt the butter in a large pot over medium-high heat; cook the celery and onion in the melted butter until tender, about 5 minutes. Add the flour and allow to cook until absorbed, about 2 minutes more. Slowly stir the half-and-half and water into the mixture. Dissolve the bouillon in the liquid. Stir in the chicken, buffalo wing sauce, and Cheddar cheese. Season with salt and pepper. Reduce heat to medium-low. Stirring occasionally, allow the soup to simmer until the the cheese has melted completely, about 10 minutes.
