There was no right in law to ride a bike on a bridleway until the the Countryside Act 1968 was passed into law.
Section 30 states “Any member of the public shall have, as a right of way, the right to ride a bicycle, not being a mechanically propelled vehicle, on any bridleway, but in exercising that right cyclists shall give way to pedestrians and persons on horseback.”
My bold.
The above law applies equally in both England and Wales; bridleways are only 'a part of the cycle network' inasmuch as it is legal to ride a bike on one. The other legal users have absolute priority and there is no requirement whatsoever to make a bridleway 'suitable for bicycles'. South Wales is no different to any other part of Wales in respect of the Countryside Act 1968.
Of course people did ride bikes on bridleways before that; in many places it was common, in others it had to be done with discretion but as it was never many people and generally very low-impact, it was broadly considered acceptable.