Put collard greens in a pot full of lightly salted water; bring to a boil, reduce heat to medium-low, and cook until tender, about 1 hour. Drain.
Cook bacon in a large skillet over medium-high heat until crisp, about 10 minutes. Drain the bacon on paper towels.
Melt butter in a large pot over medium heat. Cook and stir onion in melted butter until tender, 7 to 10 minutes. Stir bacon, chicken bouillon, water, garlic, oregano, thyme, and savory into the onion; bring to a boil. Stir collard greens into the mixture and simmer 5 minutes. Pour milk over the mixture, stir, and cook another 5 minutes.