Place green beans into a pot with enough water to cover. Add baking soda to the water; bring the mixture to a boil, reduce heat to medium, and cook until green beans are nearly tender, 7 to 10 minutes. Drain water from green beans; set aside.

Place potatoes into a large pot with 2 cups water or enough to cover; bring to a boil, reduce heat to medium, and continue cooking until almost tender, about 20 minutes. Remove from heat, but do not drain the water from the pot.

Heat butter in a large skillet over medium heat. Cook onion and bacon bits in melted butter until onions are soft and translucent, 5 to 7 minutes; add to the large pot with potatoes, and add in cream of chicken soup and milk; stir until smooth. Add green beans. Season with salt and pepper.

Place the large pot over low heat and cook the soup at a simmer until hot and the flavors have melded, about 30 minutes.