Cut the bitter melon lengthwise, discard seeds and soft tissues, and slice into ½-inch slices. Place sliced melon in a colander and toss with some salt. Let the slices sit for at least 30 minutes, tossing occasionally (this helps tore move some of the bitterness).
Rinse the bitter melon, drain and squeeze dry in paper towel. Set aside.
Heat the coconut oil in a large pan over medium-high heat. Then it is hot, add the curry paste and turmeric. Cook, stirring, about 30 seconds, until mixture is fragrant. Pour in the coconut milk and whisk. Keep whisking until it reaches a boil. Add the bitter melon slices, bell pepper, lime juice, and fish sauce. Reduce heat, cover and simmer for 5 minutes.
Remove the lid and cook for another 10 minutes, until the bitter melon is tender. Stir in the tofu and tomato, and cook 1-2 minutes more. Sprinkle with green onions, and serve.