Rinse the rice and add it to a large pot with the water, teriyaki sauce, soy sauce, garlic, and ginger. Stir to combine.
Bring the mixture to a boil over medium-high heat, then reduce to low. Cover the pot and simmer for 10 minutes.
Add the broccoli florets, sliced carrots, and bell pepper to the pot. Stir gently, then place the salmon fillets on top of the rice and vegetables. Cover and cook for another 12 to 15 minutes until the rice is tender and the salmon reaches an internal temperature of 145°F.
Remove the pot from the heat. Let it rest for 3 minutes before fluffing the rice around the salmon.
Divide the rice and vegetables into bowls, top each with a salmon fillet, and sprinkle with green onions and sesame seeds.