Hi and welcome to Seven Forums!
Regarding your query, as far as I know, this is how you do it. It is convoluted but possible.
Right then, before even opening synctoy, there are a few things you need to do.
Open up any folder on your computer
Go to organise -> Folder and search options
Click the view tab
Check show hidden files and folders
Uncheck hide protected operating system files (recommended)
Press OK
Now you're ready to open Synctoy! Ready, lets go
Open synctoy and select the folder pair you want to exclude the recycle bin from
Click the small text link that says Change options
Uncheck the boxes for exclude hidden files and exclude system files if they are checked.
Click select subfolder
Wait for all the folders to appear
Locate C:\$RECYCLE.BIN in the left hand column.
Now uncheck this. This will deselect the recycle bin folder from the sync
Ok -> OK
Run the now updated folder sync
If all has gone well, the recycle bin should not have been synced across to the other drive. To check this, navigate to the $RECYCLE.BIN folder on the other drive. You are also now free to hide hidden files and protected operating system files again if you want to. I recommend it as it stops you making any stupid errors and mucking up a system folder.
I hope this helps to solve the problem and if you have any issues following these steps, feel free to ask.