I see several problems that need to be corrected and it goes beyond the distance of your bride to the wall. It is kind of difficult to direct where they are putting things to facilitate your photography, so you are going to have to adjust instead.
First, get a bounce card, a softbox or an omnibounce for your flash. You will still get shadows, but they won't be as harsh.
There is a time to bounce and a time soften. If there is nothing you can bounce off of, then soften.
Second, get the flash off the camera. The redeye in the photo tells me the flash was mounted directly on the hot shoe and the red-eye mode wasn't used. By putting the flash on a good bracket you get the flash out of the face of your subject which prevents red-eye and keep it centered over the lens which reduces shadows.
There are several different types available, I personally use the Cameraflip, but those I work with use both the flash flip style and the same one I do. It can be had for as cheap as $65.
This photo was shot in a bar on the fly using that type of setup. Notice how close the deck behind her is yet there is no shadow and no red-eye. It was an open deck so bounce was impossible. Getting the right set up will go a long way towards making your life easier. You may not use these tools all the time, but as a friend of mine was always wont to say "better to have them and not need them than to need them and not have them".
One thing that bothers me is the shadow at the bottom of the frame. I am not sure where that came from. It looks almost like a long focal length lens was used and it caused a shadow off the flash, but I can't say definitively. I would be interested in knowing what caused that. I know the SB 600 has a fairly short snout and that can cause that when used with a variable focal length lens mounted on the hot shoe in landscape. But I am guessing you used portrait orientation which caused the harsh shadow to the side and that would eliminate the possibility of lens shadow. Something blocked the flash.
Do keep in mind that you won't always be able to get rid of all the shadows. Your goal is to reduce them in a way the photo will work and the shadow is not as big a distraction.