Buses to Karato wharf and fish market area (¥220, seven minutes, frequent), and Chōfu (¥370, 22 minutes, frequent) leave from outside the station at stop 2. For Kanmon Tunnel, Dan-no-ura Memorial or Hino-yama-kōen, take a bus from stop 3 and get off at the Mimosusōgawa stop (¥260, 12 minutes); for Akama-jingū, get off at the Akama-jingū-mae stop (¥260, 10 minutes).
If you're taking more than a couple of long bus rides in Shimonoseki, pick up a one-day bus pass (ichi-nichi furī jōsha-ken; ¥720).
It's good value – a trip to Chōfu and back alone normally costs more than ¥700 – and it saves you the hassle of paying coins each time you get off the bus.
A one-day Strait Walking Ticket (kaikyō sansaku kippu; ¥360) is also available and covers the Kanmon Tunnel and Karato wharf areas, with good savings if you take more than two rides.
Buy tickets from the booth at stop 5 of the bus terminal outside the train station, or at the Karato bus terminal.