As far as I know transparent GIFs allow only totally transparent or totally opaque pixels, so translucent pixels get driven to one extreme or the other. Your white edges are the result of that. Why do you need to use GIF? It isn't generally a good format for photographic or rendered images, so unless you need to put it on a website over a variable and unpredictable background you would do better to create a rectangular composite of your image over its intended background in PS and save that in a 24-bit format like PSD, Tif or (as a copy) JPG.