I discovered that you need to change the icon of the actual Bin, not just its desktop alias - It's a hidden file in your home folder. I use TinkerTool, a free utility for Mac (
https://www.bresink.com/osx/0TinkerTool/download.php) to reveal hidden folders. Once you have relaunched the Finder from TinkerTool, click on the Bin folder and change its icon In your home folder. You can then change the icon of the Bin alias on your desktop. Then use TinkerTool to re-hide the Bin folder.