When I enter the information into the sharing field and hit add, I get a notification that it is “Sharing with libraries…” but when the notification goes away, the collection has not been shared.
By clicking "add" you are adding that specific institution to the list of institutions that currently have access to the collection. This means that the specified institution still has to select the collection in their WorldShare Collection Manager.
It may take between 24-48 hours after the sharing selection has occurred on both ends for the collection to display as shared.