To update your Photobucket album privacy settings on Mobile Web, look for the eye! Next to each album name, including My Bucket, you will see either an eye icon, or a crossed-out eye icon.
To change the privacy settings of your albums:
Tap on the album
Tap on the eye icon on the right side of the screen.
From there you can toggle the privacy settings.
When the eye icon is normal, this shows the album privacy is set to Public
When the eye icon is crossed-out, this shows the album privacy is set to Private
