In a medium saucepan, bring 4 cups salted water to a boil. Add the wild rice; return to a boil. Reduce the heat, partially cover and simmer until rice is al dente, 30 to 50 minutes, depending on the variety. Drain.
In a large skillet, melt 4 tbsp. butter over medium heat. Add the mushrooms; season. Cook, stirring occasionally, until the liquid evaporates and the mushrooms begin to brown, about 8 minutes. Transfer to a bowl.
In the same skillet, melt the remaining 4 tbsp. butter. Add the onion, carrots, celery ribs, garlic and bay leaves; season. Cook, stirring often, until vegetables are soft, 4 to 6 minutes. Add the white rice, wild rice and 1 3/4 cups water. Cover, bring to a boil, then reduce heat to low and simmer until rice is tender, about 18 minutes. Discard bay leaves.
Stir in the mushrooms, half of the celery leaves and the chives; season. Sprinkle with the remaining celery leaves.