Bring a large pot of water to a boil. Add bok choy (in two batches, if necessary), and cook until tender, 5 to 7 minutes. Drain in a colander; let stand at least 5 minutes. Transfer to a serving dish.
Meanwhile, cook ginger and garlic in oil in a small saucepan over medium-low heat, stirring, until ginger and garlic are soft, about 8 minutes. Add tamari and oyster sauce; cook, stirring, until heated through, about 30 seconds more. Pour sauce over bok choy; toss to coat.