If I arrive at taoyuan intl airport at 11:00 at nigt, is there a direct bus service to Kaohsiung?

No, there is no direct bus service to Kaohsiung from the airport. You are advised to spend one night at the Novetel Hotel at No. 1-1, Terminal South Road, in the airport.

The next day, take a shuttle bus to THSR station for TWD30. The bus is available from 6:15 to 22:50. Then, take a high speed train to Zuoying from Taoyuan High Speed Railway Station for TWD 1,455. The train is available from 12:21 to 16:57, and the duration is about 1.5 hours. Upon arrival, take metro to the downtown area of Kaohsiung. :)