Bus Station is on Zhongxiao W. Road Sec 1, Between Taipei Main Station Front Mall Exits 8 and 9. You can see the Taipei main Station behind this Bus Station.

Alternative Bus Service to Airport early in the Morning:
http://www.airbus.com.tw/busline/airbus-ka.php
King Bus/Kuo Kuang Bus Co.
Left Baggage Center at Taipei Main Station:
Time: 8 am to 8 pm daily - 365 Day
Exit East Entrance , cross road at traffic light near the taxi stand. Keep walking downthe road passed the Parking Lot and turn left into the lane. Baggage Center there on your Right.
Rates: NTD17/- for the First 10 days. Add NTD34 for every additional day, onwards from the 11th day