In the basement of the Taipei City Hall MRT station is a Bus station. It was great to find it. It isn't big but it is nice and quiet. Even though we were in Taipei on a busy day over Chinese New Year there was hardly anyone there. It cost me NT$260 for a ticket to Taichung train station. It was NT$100 cheaper than my train ticket to Taipei in the morning.
There are a few bus companies that use it. I used All-bus. Check out the pictures to see what services are available to where. The people at the desk were helpful, I used the little Chinese I know to ask for tickets. They were really nice.