Mix turkey, bacon, onion, bell pepper, and jalapeno pepper in a baking dish.
Bake in preheated oven, stirring occasionally, until the turkey is completely browned and the bacon is crisp, about 15 minutes.
Stir kidney beans, black beans, tomatoes, chili powder, cumin, salt, and cayenne pepper together in a large pot; bring to a boil and reduce heat to medium-low.
Stir turkey mixture into the beans mixture. Cook chili at a simmer, stirring occasionally, until the beans are tender, about 40 minutes.