From Over Monnow, King Henry V Drive bus to Newport, Castle (Newport Castle). 52 min £6. From Monmouth, Bus Station (Monmouth Bus Station) bus to Chepstow, Bus Station (Chepstow Bus Station) then bus to Newport, Market Square. 1 h 35 min £8. From Monmouth taxi to Newport. 26 min £110. From Monmouth drive to Newport. 26 min £4.