To get the links, while viewing the pic in your photobucket library, you press the black bar at the bottom (with the semi-colon type symbol) and that pops up a menu with "view links" as an option. Pressing that brings up the 4 kinds of links as pictured above. Pressing on one of them copies it to clipboard in the same way.
Uploading pics to photocbucket is easier with the android app. You can do it the same way as above (open the app, go to the upload section and select them etc) but it's also embedded, so you don't even need to go into the app.
When you're viewing a pic in gallery or from the camera, tap on it and a menu pops up at the bottom. One of the options is 'Share', select that and one of the options will be photobucket. Select that and it auto-uploads the pic in the background (it opens the app, queues the upload and then returns straight to the pic you were last viewing in gallery)
FWIW: I CANNOT get the photobucket app to work on Lisa's iphone 5. It just refuses to accept the log in details.
And nope in case anyone jumps on that comment... I'm not saying android's better. I actually prefer iOS but the screen's way too small on iphone's for me, windows mobile can absolutely go drokk itself after the way they treated previous winmo customers, so that's why I ended up with Android (htc OneX)