Long-distance cyclists are essentially limited to Hwy 11. South of Hualien, that's pretty busy through Yanliao, and there's a long tunnel north of Shuilian that is unpleasant for two-wheelers. However, thereafter the route is relatively lightly trafficked until Taitung.
Heading south from Hualien, overnight stopping points are typically Shihtiping (80km) then Chenggong or Donghe.
From Guangfu Hualien Bus 1125 runs five times daily to Fengbin via Rte 11甲 (NT$67, 35 minutes)
From Hualien Roughly hourly Hualien Bus services run to Jingpu, some continuing to Chenggong.
From Taitung Diingdong Bus routes operate roughly hourly to Taiyuan, Chenggong or Jingpu, all driving via Dulan and Donghe. These are also stops on the Taiwan Tourist Shuttle bus linking Taitung to Sanxiantai via Chenggong.