STOVETOP: Bring broth and water to boil in medium sized pot. Once boiling, add rice, bay leaf, and butter and bring pot back to a boil. Boil for 2 minutes, then bring heat to low.
Evaporate the liquid (about 10-15 minutes) in pot uncovered, then add lime zest, juice, and cilantro and toss together. Season to taste with salt and pepper (I'd say about ¼ teaspoon salt and ¼ teaspoon pepper).
RICE COOKER: Add rice, then as much liquid (broth and water) as per your rice cooker's instruction. Add butter and bay leaf. Let cook until done, then add cilantro, lime zest and juice. Season to taste.