Combine mayonnaise, lime juice, wasabi paste, 1 clove garlic, and 1/2 teaspoon ginger in a small bowl. Add just enough water to give dressing a drizzling consistency. Season with salt and pepper.
Heat 1 tablespoon oil in a 12-inch skillet over medium heat. Add white parts of the scallions, 2 cloves garlic, and 1/2 teaspoon ginger. Stir until softened, about 2 minutes. Add bok choy and 1 tablespoon water. Cook until leaves wilt, about 3 minutes. Season with salt. Transfer bok choy mixture to a plate.
Heat remaining 1 tablespoon oil in the same skillet over medium-high heat. Pat salmon dry with paper towels; season with salt and pepper. Place salmon skin-side down in the skillet. Cook until skin is crispy, about 6 minutes. Flip salmon and reduce heat to medium. Cook until flesh is opaque, about 4 minutes more.
Transfer salmon to serving plates; drizzle wasabi dressing on top. Garnish with green parts of the scallions. Serve bok choy mixture alongside.