Warm oil in a large saucepan over medium heat. Add onion and bacon and cook, stirring often, until starting to brown. Add rice to pan and stir to coat in oil. Pour in wine and cook until evaporated, about 3 minutes.
Mix 2 cups hot water into broth and stir into rice in 1/2-cup increments (let each absorb before adding next). Stir, adding more hot water if needed, until rice is tender, 15 to 20 minutes.
Remove from heat and quickly stir in cheeses, salt, and pepper. Top with a sprinkle of chives.