It's easy, but you have to use the "Rich Text Editor" found when you click the "Preview" button next to the "Submit" button.
Go to your Photobucket.com image page and click on the "Share this code" box that says "Direct Link". This will copy that text to your clipboard.
On this forum editor, click on the button that looks like a scene of a tree. It's called "Insert/edit Image" if you hover your mouse pointer over it.
Paste the previously copied link into the URL box. Add a description that shows up if someone hovers over your picture. You could add a border or change the displayed size there, too. And some other things. It's better if you make your original image no bigger than 640 x 480.
I did the "Western Mouse Trap" below from Photobucket and added a border of 2 pixels.