Heat oil in a large skillet over medium heat. Add onion and red bell pepper; cook and stir until soft, about 5 minutes. Reduce heat; stir in green salsa. Add vegetarian crumbles; cook and stir to break up the crumbles, about 5 minutes. Stir in water and refried beans. Season mixture with cumin, chili powder, and garlic powder. Simmer until flavors combine, about 5 minutes.
Divide iceberg and radicchio among serving plates. Top with rice. Scoop hot mixture over rice. Garnish with sour cream and Monterey Jack cheese.