From Fishing Bridge I'd exit Yellowstone's east gate through Cody to Greybull, then take Hwy 14 to Ranchester and I-90 to the Little Bighorn Battlefield. I don't think it would take any longer than driving across the Park to West Yellowstone and then going north to I-90, and it would be a much prettier drive.
That's just seat of the pants guessing. Mapquest should give you a good idea of time and distance both ways.
(I'm assuming your question was whether to cross the Bighorns or see the Battlefield, right? Not the Battlefield or Devils Tower.)
