Whisk the barbecue sauce, chili-garlic sauce and 1/3 cup water in a small bowl; set aside. Heat 2 tablespoons vegetable oil in a large nonstick skillet over high heat. Season the shrimp with salt and add to the skillet. Cook, undisturbed, until lightly browned and starting to curl at the edges, 2 to 3 minutes. Flip and continue cooking until just opaque, 1 to 2 more minutes. Remove to a plate.
Add the remaining 1 tablespoon vegetable oil to the skillet. Add the bok choy, season with salt and cook, stirring occasionally, until bright green and crisp-tender, about 3 minutes. Add the barbecue sauce mixture and the shrimp. Toss until evenly coated and heated through, 30 seconds to 1 minute.
Heat the rice as the label directs. Top with the stir-fry and serve with lime wedges.