I just checked Photobucket again. When I hover over the small pics in my 'Library', I get a 'Hand Pointer' & a 'Gear Icon' on the upper right. I don't know why there is a difference between what you see & what I experience.

That said, I have stumbled upon a less cumbersome way to get to an 'IMG Code' option with what I'm seeing:

'Left Click' on the 'Gear Icon' & select 'Get media links' from the menu. A pane opens up showing 4 options - 'IMG Code' is at the bottom.