Place carrot into a bowl, and fill with about 1/4 inch of water. Cover with plastic wrap, and cook in the microwave for 2 minutes, or until soft. Drain.
Mash beans and steamed carrot in a large bowl. Mix in green pepper, onion, salsa, bread crumbs, and whole wheat flour. Season with salt, black pepper, and chili powder. Add flour to create a firmer mixture, or more salsa if the mixture is too stiff. Form mixture into 8 patties, and place on a greased baking sheet.
Heat a large skillet over medium-high heat, and coat with cooking spray. Fry the patties for about 8 minutes on each side, or until browned and firm.