There are several ferry lines linking Bornholm to the continent, but the commonly used by foreigners is the one that links Ronne with Ystad, in Sweden, in about 75 minutes.
The other internal line, to Kogen, takes more than 6 hours and is only made overnight. There are also lines to Poland and Germany.
To go to Ystad you may do it by car (using the Oresund bridge), by train or by bus from their stations in Copenhagen.
The island of Bornholm is a cycling paradise. All around the island one can find plenty of cycling paths that are separated from the normal roads. There are shops available to hire bicycles and at the tourist information centres one can purchase maps with an overview of all cycle paths.
Being an island without bridges to the mainland Bornholm can only beach reached by ferry or ship. The closest mainland is Swden and the port of Ystad. However there are also ferry services to Sassnitz (Germany), Swinoujscie (Poland) and Kolobryeg (Poland). During high season ensure that you book in advance since some of the ferries might be full.
Rønne is the main port of arrival for most ferries to Bornholm (and also has the island's main airport) so whether you come from mainland Denmark, Sweden, Germany or Poland you end up here. The exceptions are the summer ferries from Sweden to Allinge and Poland to Nexoe. See my Bornholm page for more detailed information.
The island offers a good network of roads that circles the island as well as crosses it on a number of places. Good signage is available throughout the island.