Watch that that toolbar also isn't spyware though
Though removing the icons like ownage says is as simple as right clicking and doing that anyway.
I tried to find a way of hiding only the recycle bin too, though I don't think its possible.
TweakUI though, would it stop the recycle bin working completly? This seems rather bad since its quite a good safety measure if you have it. At least if you deleted something important, you know for sure if its not too big it wouild have been thrown into there before being deleted (at least to windows) from the drive.
Can't you just place it on the top right? Or even move that shortcut to a position in my computer or something, and not having it on the desktop