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 - although usually you won't find any Norwegian immigration officers in the island to refuse your entry! But, if you absolutely have to get there anyway, 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. If you have a useful occupation or skill, such as Arctic research biologist, research geologist, helicopter pilot, or physician, you will probably be welcome. There's been at least one case of this happening in the past, when a bunch of radio amateurs were allowed to enter the Island for a DXpedition setting up an amateur radio station there to communicate with people across the world.
Companies that can help to arrange travel to Bouvet Island include:
Oceanwide Expeditions(http://www.oceanwide-expe...) explores the most remote places in and around the South and Mid-Atlantic Islands with their own ships and expedition crew. Passengers are taken from Ushuaia to remote locations such as Bouvet Island. Other locations are the South Sandwich Islands, Ascension Island, Tristan da Cunha, Cape Verde and St. Helena. With fully equiped zodiacs passengers are going ashore on several islands, which are rich in wildlife and offer plenty of opportunities for exploring activities.
There is nowhere even remotely usable as a harbour, although it is possible to anchor offshore. If you are willing to put your life at risk, you might try using a light boat with outboard engine to enter. It has been known to work, but plenty of people have tried and decided it was not worth the risk.
In theory, it should be possible to land on the island using a large, dual engine speed boat, as there is a small beach in the North Western corner of the island. It would, however, require extraordinary bravery and considerable boating skills to avoid sinking the boat before reaching shore.