Place turnips into a saucepan with the water and 1/2 teaspoon salt. Bring to a boil over high heat, then reduce heat to medium-low, cover, and simmer until the turnip is soft, about 5 minutes. Once tender, stir in the kidney beans, and cook 5 minutes more.
Meanwhile, heat the vegetable oil in a skillet over medium-high heat. Stir in the cumin and fennel, and cook until the spices toast and become fragrant, about 1 minute. Stir in the onion, and cook until it turns golden brown, about 5 minutes. Stir in the minced ginger and garlic, cook and stir for 30 seconds, then add the tomatoes and salt, and continue cooking until the mixture turns pasty. Finally, stir in the paprika, turmeric, ground ginger, and 2 tablespoons water; cook 2 minutes more.
Add the tomato mixture to the turnips, and simmer 10 minutes. Season with garam masala before serving.