You have to set your albums to private in photobucket if you don't want them to be viewed by random people :) just use Dropbox if you want to ensure privacy...
Can people see the pictures of my girlfriend I have on photobucket? Im not sure if only I am able to see them or if other people can that search. It shows me a number of views for each picture and it keeps increasing even without me clicking on them.
Usually those public sites you set private meaning people visiting your profile dont see the private photos, but the direct link can be viewed by anyone you give it to. And you of course can see them. Public is where you see them and others visiting your profile.
Its been forever since I used photobucket! But this seems like the general works of it now days. Its not very private either way, obviously.
This should answer your question: Photobucket Privacy Settings