Oh, the dragon...no thanks. I'm not going to take a chance. I've seen it and I'll die no doubt
You have no choice.
Drake is rather easy to avoid. Sprint forward on the bridge just enough to trigger its appearance (you'll hear it coming), then run the hell back and steer to the side immediately. After that, it shouldn't breathe fire at you until you get at least to the staircase, where you can easily avoid the fire.