The poo on the bottom of the cup in the picture you linked looks ok, I don't see white poo it looks brown to me in the picture. He may improve once he adjusts to the bigger tank of heated water too. It could be he's had an ammonia buildup in the cup in the store, but i'm not sure. I've never had exact symptoms like your guy has.
I would keep his tank bare bottom though for now. Maybe put something in there he can sit on that can be cleaned.
I'm by far
no expert on fish diseases and spend hours looking up symptoms. Here are a couple good disease sites if you don't have them, that have helped me.
--This site is good imo (you have to click the links on it that say continued on the next page
, which is a pain but it has good info on a LOT of diseases, both for bettas and every fish.)
--Fishy Portal (another decent site to have on hand just in case imo, I don't have a microscope or any way to use the bacteria ID part of the site but the rest of the information helps.)
And of coarse searching the disease forums here on bettafish, and TFK and google/bing. ;)
Hope your new guy feels better.
From the picture though he looks beautiful. I can't find any other pictures of him. You don't have any albums here and i'm too dumb to figure out how to search a photobucket album out of a single picture link lol but i'd like to see some additional shots of him.