Clicking on every image to access the link, then the link doesn't even WORK !!

I'm not sure why the link wouldn't have been working, but you can now have all the links you use displayed on the page (without clicking on individual images) in the new Photobucket.

Sign in and pull up the dropdown menu under your user ID, click User Settings, then the Albums tab. Towards the end of the options displayed, check the box for Turn on easy linking mode and save. It doesn't work exactly the same as before (at least not for me), in that one click automatically copies the link or code. I find I now have to click on the link field, then right click to select copy.

As dave mentioned, if your albums aren't private, anyone can view and get links to your images.