Yes there is, at least if you leave from Osaka. We paid 40 EURO (for one bike), even though we suggested to take the wheels out and wrap them up in plastic bags. In a hard suitcase it should be possible, but then again it might cost you some money for 'excess luggage'.

If you plan to go cycle there, we can really recommend the Shikoku island, we did the cost line (southwards) and had two great cycle weeks.