I did some looking into this before and there are some sites kicking about with information.
Heres something I just found quickly (it's from 1999 but should still be similar process but prices are bound to be different).
QUOTE:
Driver's License Info
Unlike in some American States, you must carry your license with you at all times if you're operating a motor vehicle. You must also carry the title of the vehicle on the bike, (i.e. the insurance form). A non-Japanese license is not a valid license in Japan -- you must have either a Japanese license or international permit.
INTERNATIONAL If one has an international driver's permit with a motorcycle endorsement and your country's valid license, one may drive any size motorcycle. Japan only allows the use of an international permit for up to one year after your latest entry into the country (even if the international license would otherwise not be expired).
CONVERSION FROM A NON-JAPANESE LICENSE A foreign license may generally be converted to a Japanese license. Any international license, or lack thereof is irrelevant. Note: Non-Japanese must have been in the issuing country for three months after the last-date-of-change on the license for it to be convertible in Japan. For Japanese, the three months become six. A motorcycle endorsement converts to a mid-class motorcycle license.
Basic conversion method: Bring alien registration card, passport, foreign license, and about 2,500 yen to a JAF (Japan Automobile Federation, much like the AAA [American/Australian Automobile Association]). They will "translate" your license, and give you some paperwork.
Bring it all to your prefectural licensing center, stopping at one of the photo shops that should litter the nearby area to get two license standard size photos (3cm x 2.4cm.... they'll know what size to give). B/W ok. Note that neither of these photos will actually appear on the license. I have no idea what the photos are for.
Bring it all, and about 7,000 yen (cost depends on various factors) to the licensing center and fill out appropriate forms. You might have to take a practical test, I'm not sure. Recently, converting a car licence changed to requiring a test (make sure to not hit the cones, and use your mirrors "appropriately") Do what they tell, pay what they want. Receive license. Valid for three years, expiring on your birthday.
DOING IT THE JAPANESE WAY Getting a scooter-only license is apparently trivial. Getting a motorcycle license (mid-class or big-class) is rather difficult, and apparently an exercise in patience and frustration (and money).
More information can be found:
Here
If link is not allowed I will remove. You can get to similar sites by googling 'riding motorbike in japan' or something to that effect