Bus
Until recently, it was difficult to recommend buses as a major mode of transport for cyclists. Taking your bike on regular commuter buses would be a struggle for any but the most forgiving driver, since you'd have to take the bulky bagged bike on the bus with you (no luggage space below or on top). And until recently, long-distance buses were relatively few and far between, and generally had no on-board toilets, making long journeys less than comfortable. As a result, until relatively recently you were pretty much limited to trains, ferries and (gasp) planes as a way of getting to your starting point.
However, in Kansai at least, there has been something of a revolution in long-distance bus travel - no doubt due in part to the completion of the Akashi Kaikyo Bridge leading to the island of Awaji. It is now possible to go by bus across that bridge, down through Awaji and across the Naruto Bridge to Shikoku - so any destination on the island of Shikoku is a relatively short bus ride from Kansai (generally no more than four hours). (Note that cycling across the Akashi Kaikyo Bridge is NOT an option; the only Inland Sea bridge system across which it is possible to cycle is the Shimanami route further west.). Buses also go to many parts of Honshu - for example, from Kobe to Okayama and Hiroshima - and even further (for example, to Nagasaki on Kyushu).
Long-distance buses almost always have luggage space down below where you can stow your bike. Prices are usually (but not always) much cheaper than the expensive JR trains - in terms of bang for buck, about the same as a ferry but generally much quicker. Long-distance bus is now the best way to get to many destinations, so be sure to check out this option. Check with a travel agent or go to the main bus station in any major city. Some buses run overnight, like the night bus that runs between Tokyo and Kyoto. (Note: in virtually every case, a long-distance bus will have a bathroom at the back.)
Note that some relatively far-off coastal destinations - Beppu on Kyushu, for example - can be reached by long-distance bus but are also served by excellent ferry routes, so ferry would probably still be your best option.
For other reference materials that you may find useful in route planning, see RESOURCES.