In a large saucepan, cook bacon over medium heat, stirring often, until crisp, about 5 minutes. Transfer with a slotted spoon to a small plate. Add zucchini to pan and cook, stirring occasionally, until lightly browned, about 2 minutes. Transfer, using a slotted spoon, to plate with bacon.
Add onion to rendered fat in saucepan. Cook, stirring, about 4 minutes, until golden and softened. Stir in beans and broth and bring to a boil over medium-high heat, stirring occasionally. Reduce heat and simmer soup for 15 minutes.
Coarsely mash beans with a potato masher to thicken soup slightly (do not overmash). Stir in reserved cooked bacon and zucchini and simmer for 2 minutes to blend flavors. Stir in chives and season with pepper. Spoon soup into bowls and serve with dollops of yogurt.