There is an FAQ section on photobucket...
"How do I allow friends & family to view my album?
If your account is public:
* Give your username to your friends and family.
Have your friends and family:
1. Go to the Photobucket home page.
2. Enter your username in the Search box.
3. Click the Search button. A link, "view username's album", displays.
4. Click the link. The viewer is taken to your public account.
You can also allow your guests ?read-only? access, via password, to your entire Photobucket account or to specific sub-albums within that account. You can make your account or specific sub-albums within it private and assign guest passwords. To assign guest passwords for private sub-albums, the main account must be set to public. All content in the main album can be viewed by anyone.
See the topic How do I change the status of sub-albums? and the Changing Your Album's Privacy Settings tutorial for information on changing the public/private status of an album.
See the topics Is a password assigned to my private sub-album? and How do I share a guest password? for information on sub-album passwords.
If you have trouble setting up a guest login, see the Troubleshooting: Guest login section."