What level are you and where do you live? There are a lot of cycling/triathlon groups out there, they are either organised by bike shops or by individuals who have got their own group going. Most rides start out in the north, Tianmu or Danshui, and either go over Yangming Shan, or around it to Jinshan on the north coast. Tianmu folk are often expats, while I've found that my local contacts tend to start around Danshui. Not sure why there's such a distinction. maybe coincidence.
The groups I've ridden with, hardcore or not, are all very welcoming, but it's a lot of pressure to keep up at speed for 100km when you are not fit like me!
I have only been 5 or 6 times in the past 5 months since I arrived because the rides start early and I don't have a car so I have to get there by MRT. I am not a morning person
so a 7am start would mean I get up at 530 am to reach Tianmu. Some people start at 5 or 6am! I live in Guting and would love to find a few rides starting from this area.
I am out of shape and really want to get back into it so if you are around my area, please contact me...
Hope this helps.