This is thought to be the most remote, uninhabited island in the world, where only seals and penguins dare to live. It is actually owned by Norway, but its nearest neighbour is Antarctica, over 1609 km away from it. Its biggest celebrity claim is that most of Alien vs. Predator was filmed here.
There is no accommodation on Bouvet Island. The only permanent structure is an automated weather station! How cool!
According to wikitravel.org, since the entire island is a nature reserve, it's likely that you will be denied entry permission, if the purpose of entering is just tourism! But, if you absolutely have to get there, your best bet is to try to find out when the next research expedition is scheduled to get there and ask if you can join them :)