Hi Norman,
Well it's about 12 miles, so could be done by pony & trap. But more likely by rail, as all the area's railway companies were offering passenger services at about that time. Start at Parkend to Coleford on the S&W Joint Railway, then Coleford to Monmouth by GWR line.

See https://en.wikipedia.org/wiki/Severn_and_Wye_Railway

and also maybe http://www.deanweb.info/history2.html