Sun Moon Lake is a beautiful place. Although it's not a big place, you still need some trafiic tools. Bicycle and shuttle boat is one choice to travel SML, and Lake-sourrunding Bus is another choice.
According to official announcement, you can get on the bus on the route anywhere, anytime, as long as you wave your hand and notify the bus driver.One day ticket for the Lake-sourrunding Bus costs 80 NTD.
Here are the Bus Time Table in English and in Chinese (正體中文版), and the following is the map for every stops. As for the way to get SML, you can refer these two pages: Renyou Bus and Nantou Bus.
Sun Moon Lake Surrounding Bus Stops Mapping:
在較大的地圖上查看Sun Moon Lake Surrounding Bus Stops