At that time of day on a Saturday the roads should be fairly quiet.
I’d suggest not charging up the taff trail as it’s shared use rather than a dedicated cycle lane.
There are offroad subways to get across the Gabalfa interchange, but I tend to just go round the roundabout, it’s 20mph and will probably still be quite quiet on Saturday morning 7-8am.
The A470 gets a bit fast and furious just before Tongwynlais, I don’t know how to direct you passed that, but I’d probably drop onto the old cardiff road a4054.
The otehr option would be to stay on the Western side of the river all the way out of Cardiff into Gwaelod and Taffs Well.