I’ve taken buses from Taipei to Central Taiwan and to Southern Taiwan.
All I can say is: “Don’t do it.”
Believe me, you don’t want to spend 8 or 9 hours on a bus when you’re going on holiday – or any other time, for that matter.
Take a plane from Taipei’s municipal airport to Kaohsiung’s airport. Planes are leaving all the time.
If you don’t have time to book a flight with an agent or airline, you can practically walk into the aiport and have your choice of flights.
From the Kaohsiung airport it is quite easy to get a bus to Kenting (about 90 minutes in good traffic.)
Believe me, it is worth the price.
If you really don’t want to take a plane, take the train to Kaohsiung.
6 to 8 hours on a train is better than on a bus.
The bus station in Kaohsiung is next to the train station. From there you can get a bus to Kenting (about 90 minutes in good traffic).