From Japanese websites
Shimonoseki to Busan
9,000 yen per person 2nd class one-way
Motorcycle 48,000 yen (price for round trip only shown as Japanese are required to book round trip to bring their bike back to Japan)
Hakata to Busan
9,000 per person 2nd class one-way
Motorcycle cost not listed on website (but probably about the same at Kanpu Ferry)
Note that these ferries usually only carry vehicles registered in Japan and Korea (neither has a land border with a friendly country) and it may take more time for procedures with vehicles registered in other countries. I asked Kanpu Ferry a few years ago about vehicles from other countries, and they said it was OK, but will require more paperwork. So, I would advise that you don't just show up at the port an hour before departure and expect to get on the ferry right away.