WOW! You just gave me an education. I know my photbucket is set to private, but now I wonder if the way you described can be done irregardless.
Ok I just tried it while I am logged out.
I retrieved the following link from my post of items for sale:
If you paste that link in the address bar, you bring up just the photo.
Now per your instructions, I erased the /135.jpg to see if it would go to my albums and it took me to the login screen for photobucket.
I have my privacy settings on photobucket set so that no one can view. It looks like the security also addressed the vary thing you just listed out, so if you change your privacy settings your pictures should be just fine.