All bitly links are permanent and can never be redirected or deleted.
If you'd like to remove a link from your bitmarks list, you can archive the link. Archiving means you will no longer find the bitly link in the 'your stuff' view or via search. To archive a bitly link, click on the check box next to the bitmark in the 'your stuff' view and click on ‘archive’ in the orange bar that pops up. You can also click the 'X' that pops up on the top right when you hover over a shortlink.
To view all your archived bitly links, go to the search bar in ‘your stuff’ and click on the drop-down arrow. From there, you can select ‘your archived bitmarks’ and view all the bitly links you’ve archived. See one that you’d like to unarchive? Hover over the shortlink and click ‘unarchive.’ It will appear in your stuff view on the date you first saved it and become searchable again.