In a small bowl, mix together the teriyaki sauce, sesame oil, grated ginger, and minced garlic. Place the salmon fillets in a shallow dish and pour the marinade over them. Let marinate for at least 15 minutes.
While the salmon is marinating, cook the jasmine rice according to package instructions. Once done, set aside and keep warm.
In a large skillet over medium heat, add a splash of sesame oil. Add the chopped bok choy, sliced red bell pepper, and julienned carrot. Sauté for about 5-7 minutes, until the vegetables are tender but still vibrant. Season with salt and pepper to taste. Remove from heat and set aside.
Heat a non-stick skillet over medium-high heat. Remove the salmon from the marinade (discard the marinade) and place them skin-side down in the skillet. Cook for 4-5 minutes on each side, or until the salmon is cooked through and flakes easily with a fork.
In serving bowls, layer a scoop of jasmine rice followed by the sautéed vegetables. Place a salmon fillet on top of each bowl.
Sprinkle chopped green onions and sesame seeds over the salmon and vegetables for added flavor and crunch.