It is quite far from Taichung to Jiufen. If it is cheap, it will definitely take a lot of time. You can take a bus to Taipei and then transfer to Jiufen. The bus to Jiufen does not run frequently a day, so pay attention to the timetable!
The most convenient way is to take the train from Taichung Station to Taipei, then take the train from Taipei Station to the direction of Yilan, then get off at Ruifang Station, cross the road at Ruifang Station, and take the bus to Jiufen Jinguashi
The cheapest way: Take a bus from Taichung to Taipei Main Station (less than NT$200), the journey takes about 2.5 hours. After arriving at Taipei Main Station, transfer to the local train of Taiwan Railway to Ruifang. The journey takes about 40 minutes. Get out of Ruifang Station and take the bus opposite to Jiufen. The journey takes about 15 minutes. <br/><br/>If you want to connect easily from Taichung to Taipei, you can take the train or high-speed rail, but the bus is still the cheapest.