Place a colander on top of a bowl; add salmon to the colander and separate fish a bit to allow it to drain. Let stand until well drained, about 10 minutes. Discard juice and transfer salmon to a large bowl.
Mix bell pepper and onion into the salmon. Add bread crumbs, eggs, soy sauce, Sriracha, ginger, 1 teaspoon sesame oil, mustard powder, and garlic powder; mix to combine. Form into 5 patties. Place patties on a cookie sheet and cover with plastic wrap. Chill in the refrigerator, 1 hour to overnight.
Heat vegetable oil and 1 teaspoon sesame oil in a 12-inch nonstick skillet over medium-high heat. Gently place burgers into the skillet, reduce heat to medium, and cook, turning just once, until well browned, 7 to 9 minutes per side. Place cooked burgers on a serving platter.