I'm not familiar with Photobucket, but at many "picture sites" you can click on a picture to get the "big view" which sometimes is the original or sometimes just a larger "reduced" image that meets some arcane site requirements.

If the URL shown in the address bar on your browser changes when you click to the "big view" that's probably the "address" that you can copy and insert into a link on your website. (????)

The best format for the html you'd want on your website, both to display the picture and to send viewers to the bigger version, would be best left to someone with better web page design knowledge than I can offer; but confirming that you know specific addresses for the images you want should be of some help.

John