While noodling around Windows' Group Policy Editor, I noticed that you can hide the Recycle Bin in the desktop:
- Start Group Policy Editor using gpedit.msc.
- Select User Configuration / Administrative Templates / Desktop.
- Select Remove Recycle Bin icon from desktop.
- Select Enabled radio button.
Note that Windows' Group Policy Editor is generally used to turn off features, so enabling a setting generally means to disable a function.