The Recycle Bin is just a desktop link to each user's folder within C:\RECYCLER
The individual folders have names like S-1-5-21-343818398-2146017927-1417001333-13029. In Windows Explorer > Tools > Folder Options > View, you have to deselect "Hide protected operating system files" in order to see C:\RECYCLER and its subfolders.
As Administrator, you should be able to create a desktop shortcut to each user's folder and name each shortcut so that you can tell whose folder you're clearing. Do yours last ... when you delete the folders of other users, they wind up in your folder.
If you're willing to do it blind (without checking the contents of each folder) you can probably automate erasing C:\RECYCLER with Eraser.
EDIT: I should have said "... automate erasing the subfolders in C:\RECYCLER with Eraser."