I'm not a better man, I am a coward. I would lure him to the doorway he couldn't fit through and then attack when he gave up and walked away. And I was so bummed when that helmet didn't drop. Gah, I wanted it so bad.
I did however end up with a really badass sword. The red dragon is a jerk, guarding some looty things. I want the looty things! So thinking back to the red dragon in Demons Souls I decided to buy a bunch of arrows and kill the bastard. I was able to plink away at him for a bit but I didn't know if I was going to be able to kill him. He got hurt, he would fly around, so I figured I'd keep going. Eventually it sounded like I had killed him and I got a Drakes Sword or something like that. I could only 2-hand it at first but I bumped up my stats and can now one-hand it. It does some serious damage. Downside is theres no stabby motion, only a swing so its harder to use in confined hallways. But some things that used to take 2-3 hits are now dying in one, so I'm pretty happy with it.
Note, however, this didn't kill the dragon. He's still there and will roast a bitch if they step foot on that walkway.
The bow is proving itself useful, but not overpowered like it was in Demons. Those rats? I am able to draw one out onto the bridge and take care of it with a single shot, then the other two are easier to handle. So now I basically have a pretty easy straight shot to the next boss. I know what I'm in for....and I'm scared.