I'd agree with Dave on this one. The most likely problem here is that the bridge height is too low. The other possibility is that you have a high fret or warped fingerboard in the high fret area.
Getting the action to be the height you want and buzz-free is a delicate combination of relief in the neck and bridge height. If you don't have enough relief then it doesn't matter how high you raise the bridge, you'll still buzz. Conversely, if you have the bridge too low, it won't matter how much relief you dial in, it will still buzz on the higher frets. The buzz is coming from the vibrating string hitting a fretwire somewhere above where you're fretting.
I'd try raising the bridge first to see if you can eliminate the buzz that way. If you have to move it a long way (more than 1/8) then the problem is probably more serious. If the high fret action seems reasonable after raising the height, but the low and middle ranges have action that's too high, then you need to reduce the relief to bring things back into alignment.
If you really have to crank the bridge up a long way or even the high register of the neck has high action when you eliminate the buzz, then you probably need to look at the fretwork to see if there's a high fret or bump in the fingerboard, something that will probably require a pro to fix. If you're lucky, it may just be a matter of reseating a loose fret or filing the high fret down a bit. If it's really a bump in the fingerboard, then you'll probably have to refret the instrument to fix this.
In this case, you probably want to attack the bridge height first and not tweak the truss rods. If the problem was that the bridge was just sitting too low, then you'll probably end up tightening the trussrods rather than loosening them.
Good luck,
David Fung