Preheat your oven to 350°F (175°C).
In a large mixing bowl, combine the navy beans, barbecue sauce, brown sugar, ketchup, diced onion, diced green bell pepper, Worcestershire sauce, garlic powder, black pepper, salt, and smoked paprika if using. Mix well until all ingredients are evenly incorporated.
If using bacon, fold in the crumbled bacon into the mixture.
Transfer the bean mixture to a 9x13-inch baking dish and spread it evenly.
Cover the dish with aluminum foil and bake in the preheated oven for 30 minutes.
After 30 minutes, remove the foil and bake for an additional 15-20 minutes, or until the beans are bubbly and slightly caramelized on top.
Remove from the oven and let cool for a few minutes before serving.