Combine the soy sauce, Sriracha and sugar in a bowl; set aside. Meanwhile, heat 1 tablespoon vegetable oil in a large nonstick skillet over high heat. Add the Canadian bacon; cook, stirring, until crisp and browned around the edges, about 4 minutes. Transfer to a bowl.
Add 1 more tablespoon vegetable oil to the skillet, then add the mushrooms and 1/4 teaspoon salt. Cook, stirring occasionally, until the mushrooms start browning, 4 minutes. Add the remaining 2 tablespoons vegetable oil, the bell pepper and red onion and cook, stirring occasionally, until the pepper is crisp-tender, about 3 minutes.
Add the garlic, bok choy and 1/4 teaspoon salt and cook, stirring, until the bok choy is just wilted, about 2 minutes. Return the Canadian bacon to the skillet, add the soy sauce mixture and stir to combine. Serve over brown rice.