There are various places around the city for catching buses to CKS Airport. Where do you live?
At NW corner of Zhongxiao-Fuxing, in front of the Hi-Life outside Exit 1 of the MRT (Andong St.) there’s an Evergreen bus to CKS that leaves every 20 minutes, starting around 5:30am. The same bus also stops at Bade/Fuxing (SW corner) and several other locations. Fare: 135
To the west of the Taipei Train Station is a bus terminal that has Guoguang Hao buses going to CKS. Fare: 125
Outside the Far Eastern Hotel (No. 201, Dunhua S. Road Sec. 2), there’s a bus that leaves regularly starting around 4:00am - your best bet for catching early morning flights.
There’s a bus terminal at Songshan Airport at Dunhua/Minquan with CKS buses. Fare: 125