Wrap tofu in several layers of paper towels; place in a shallow dish. Place a weight over tofu. Let stand 10 minutes. Cut tofu into cubes.
Heat a wok or large skillet over high heat until hot; add oil. Add tofu; stir-fry 2 minutes or until lightly browned. Remove from pan using a slotted spoon; set aside. Add bok choy, mushrooms, and carrots to pan; stir-fry 2 minutes. Return tofu to pan; add barbecue sauce. Stir-fry 30 seconds or until thoroughly heated. Serve over rice.