overnight service, the Dream Nichirin, which ran over the same route, however this train service was discontinued on March 11, 2011 (in conjunction with the opening of the completed the Kyushu Shinkansen).
There is no charge for the above services with a Japan Rail Pass, and there is a JR All Kyushu Pass that covers all routes as well, aside from the reference to the Shinkansen in Kokura and beyond. The Kyushu Shinkansen stops at Hakata; Hakata to Shin-Osaka (including Kokura) is owned by JR West, so you would need a JR West Pass for that section.
Starting on March 12, 2011, a highway bus operated by JR Kyushu began to Miyazaki from the Shin-Yatsushiro bullet train station. The "B&S Miyazaki" (B&S for Bus and Shinkansen) will operate once per hour, timed with the arrival of the bullet trains from Fukuoka. The bus trip takes just over 2 hours from Shin-Yatsushiro at a cost of 4,150 yen each way. The overall journey from Fukuoka to Miyazaki will be shortened to just over 3 hours using this train/bus combination. The bus is not valid with the Japan Rail Pass, but bus tickets can be purchased at any JR Midori-no-Madoguchi seat reservation counter.
By bus
Hourly buses run from Fukuoka to Miyazaki in about 4 1/2 hours at a cost of �6000
