Just got Brompton bike today (S6R) and the first ride is from Bishan park to Circuit road. I took this route because from last week I have tried PCN on changi airport and it's really good. All path are in good condition and don't need to carry for crossing a road but PCN from Bishan to Circuit road is another story.
You can see my route here
I have to carry bike for crossing the pedrestrain bridge atleast 3 times and two with low ceiling under the road cause it very tired when arrived home.
I'm expected a lot better atleast don't need to carry a bike like this and have a traffic light for crossing the road.
So the best way for going to Bishan park I think is taking the MRT and go to the closest station (not sure is it AMK or Bishan) and bike from their. It will a lot easier than carry up and down.