On this page, you'll find all the information you need to travel from Kaohsiung City to Kenting National Park and the Kenting beaches by public bus.
As you've probably realized by now if you've looked at a map of Taiwan, both the high-speed rail (HSR) and normal train (TRA) don't go all the way down to the southern tip of the island, where Kenting National Park is located. The HSR only goes as far as Zuoying station in Kaohsiung City, and the TRA train will only take you as far as Fangshan Township.
By far the easiest and most relaxing way to travel to Kenting from Kaohsiung is to take the comfortable Express Bus. At Zuoying HSR station in Kaohsiung, go to Exit #2. That's where you'll find the Kenting Express ticket booth and bus stop.
The cost of a one-way ticket is 350NT$. Depending on the traffic situation, it usually takes between 2.5 to 3 hours to reach Kenting Town. If you are lucky, the ride can be as short as 2 hours.
As is expected on buses in Taiwan, the temperature can be like in a freezer, as Taiwanese like it COLD! Bring a warm sweater for the ride between Kaohsiung and Kenting, even if it's in the middle of summer and it's 35 degree celcius outside.