In 1870-72, John Marius Wilson's Imperial Gazetteer of England and Wales described Bayvil like this:
BAYVILL, a parish in the district of Cardigan and county of Pembroke; on the river Nevern, 3½ miles ENE of Newport, and 6½ SW of Cardigan r. station. Post Town, Newport, under Haverfordwest. Acres, 1,344. Real property, £1,195. Pop., 118. Houses, 29. The property is divided among a few. The living is a vicarage, united with the vicarage of Moylgrove, in the diocese of St. David's. Value, £224. Patron, the Lord Chancellor. The church is good.
GB Historical GIS / University of Portsmouth, History of Bayvil in Pembrokeshire | Map and description, A Vision of Britain through Time.
Date accessed: 27th April 2017
Click here for more detailed advice on finding places within A Vision of Britain through Time , and maybe some references to other places called " Bayvil ".