That's because it's your album and Photobucket is recognizing your IP address when you click on it. If you have your album set on "private" you can post the URL for the video and others will be able to view only that video.

Just copy and paste the IMG Code directly into your post. Here's a video of my home made ball tumbler. It's from an album that contains five other pictures.



To set your album to private, click on "Account Settings" in your Photobucket home page, then scroll down to "Album Settings" to the "My Album is" section and set it to Private. Be sure to then scroll all the way to the bottom of the page and click on SAVE.