Bring 1 cup water to a boil. Add the bulgur and simmer, covered, until all the water is absorbed and the bulgur is tender, 12 to 15 minutes.
Meanwhile, heat 1 tablespoon of the oil in a large saucepan over medium-high heat. Add the onion and bell pepper and cook until tender, 6 to 8 minutes.
Add the garlic, cumin, chili powder, 1 teaspoon salt, and ½ teaspoon pepper and cook until fragrant, 1 to 2 minutes.
Add the tomatoes and their liquid and 1 ½ cups water. Bring to a boil. Add the beans and simmer until slightly thickened, 8 to 10 minutes.
Stir the lemon juice, scallions, jalapeño, remaining tablespoon of oil, and ¼ teaspoon each salt and pepper into the bulgur.
Divide the chili among bowls and top with the bulgur.