Open Regedit & explore:

i

f you are using the XP style start menu
HKEY_CURRENT_USER\SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\HideDesktopIcons\NewStartPanel\

if working with the classic menu:
HKEY_CURRENT_USER\SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\HideDesktopIcons\ClassicStartMenu\

Inside, Make new DWORD-Value with the name "{645FF040-5081-101B-9F08-00AA002F954E}" & 'Modify' Value "1"

That will just hide the Recycle bin icon,
If a Dock is installed, by this procedure the 'Recycle bin' Docklet won't be anyhow affected as by some other Tweaks. 

To restore the desktop icon again, just 'Modify' the same DWORD-Value to "0"