Thanks to Craig for this:
You will see on each picture that you have on your photobucket, if you click it you have 4 links to the left of the picture (As below)
If you go down to IMG code and click, it will say "copied"
This is now on your clipboard, so when you go to write the post, you can right click the text box and click paste, and the link will appear, when you click post the picture will appear in the post you made.