Bring a large pot of water to a boil over high heat. Add salt and 1 teaspoon oil to water and return to a boil. Prepare an ice-water bath; set aside. Add bok choy to boiling water and cook 1 1/2 minutes. Immediately drain and transfer to ice-water bath to cool. Drain and set aside.
Heat a wok or large skillet over very high heat. Add 1 tablespoon oil to wok. Add bok choy and season with salt. Cook, stirring quickly, until bok choy is wilted, about 1 minute. Immediately transfer bok choy to a serving platter.
Drain any remaining liquid from wok and return to high heat. Add remaining tablespoon oil. Add ginger and cook, stirring quickly, until lightly browned and fragrant, about 30 seconds. Add mushrooms, season with salt, and continue cooking, stirring constantly, about 1 minute. Add 1/4 cup water to wok and continue cooking mushrooms until soft, about 1 minute more.
Pour mushrooms and cooking liquid over bok choy. Serve immediately with dipping sauce.