Mine looks different than Wades. Not sure why. Mine does not have the link areas under the pics.
On my Photobucket, If you hover over the picture with the mouse, there is a little icon that appears in the upper right hand corner of the pic. If you hover over that little icon, options appear that say "share, get links, move, edit, copy, delete". Click on the "get links" one and a box appears....it's the bottom link tagged "IMG Codes". If you just click on it, it automatically copies and then you can paste in your message.
If you're working on a picture in "edit" mode, then the "get links" tag appears with all the "share" links above the picture.