Quickest way to get to the start of the Doethie would be to take the road which then turns into a track. There is one mother of a climb soon after the tarmac finishes and it is a little boring, but still the quickest way.
You could just ride up to the Dam, do the route in the normal way and you then get the nice chapel climb at Soar y Mynydd.
Or if you have time, maybe an OS map/GPS and want some adventure, then you can also link in Mynydd Mallaen, then head through some forest track/back roads eventually getting to the Doethie. Can be hard to navigate though.
It is possible to ride off-road from Cwm Rhaeadr to the Towy Bridge… if that is what you mean?