Rinse the rice well and drain. Pour the oil into a large saucepan and add the onion and carrot. Cook over medium-high heat, stirring often, until softened, 3 to 5 minutes. Add the garlic and cook 1 minute longer. Stir in the mushrooms, bamboo shoots, and turmeric. Cook, stirring often, until the mushrooms start to give off liquid, about 5 minutes.