Photobucket has indeed changed--and for the better.
Once you've uploaded your pics to your Photobucket library and have your thumbnail photos, simply move your cursor arrow over one of these thumbnail photos. A little gear shaped wheel appears in the upper RH corner, move your cursor over the wheel and a drop down menu appears, click on "Get Links", another drop down menu appears, click on "IMG Codes" and the word "Copied" briefly appears. Then paste that into your message and
voila your image appears just like this: