Place bitter melon slices in a large bowl of water; stir in salt until dissolved. Let soak for 15 to 20 minutes. Drain.
Combine bitter melon, tofu, and bottle gourd in a microwave-safe pressure cooker.
Mix dashi stock, soy sauce, and mirin together in a small bowl; pour over bitter melon mixture. Close pressure cooker according to manufacturers' instructions and cook in the microwave at 600W for 7 minutes.
Open pressure cooker and stir in okra. Close and cook until okra is tender, about 1 minute.
Transfer bitter melon mixture to a serving plate; garnish with grated ginger.