Hi Stacy!Goodness - don't ever tell a Welsh person that Wales is part of England!You will get a VERY cool reception! Wales was invaded by the English, and there is quite a strong movement to restore their independence and the Welsh language.
There seem to be quite a few different spellings of Beard - mainly due to some very "broad" accents - and a lack of "fixed" spelling until recent times. Often the person providing the information could not read or write (often they signed with an X) - and the person writing down the information tried to spell the name which he heard e.g. one variant of Beard is Bird...another is Baard!Beard - pronounced B-ear-d is the form which my family originating in Bedfordshire use. I would hazard a guess, that your ancestors went from England to Wales, and that the earlier broad regional accent was retained.
In English records, Beard itself, and Barbe (Hugo Alabarbe)are both found as early as 1086, and the Scandinavian Skegg (Old Norse) in 1379. Compounds are descriptive of colour and shape, but few survive: Fairbard, Blackbird, Whitbread sometimes for a white beard and Goldbard for golden beard. The "Bearded Lady", remarks Ewen "is represented by Alice Barbe Dor" (1246 Northamptonshire). He did not realise that the lady was a member of a well-known Cambridgeshire family and had inherited the name "golden beard", which may survive as Barder. Among these obsolete examples we may note William Museberd 1198 PipeRolls, "mouse", Thomas Dustiberd 1229 Patent Rolls(Somerset), Peter Seilberd 1230 (from the Pipe Rolls), John Spadeberd 1246 (Assize Roll Lancashire) (1598 Oxford English Dictionery), Roger Thistilberd 1260 (Assize Roll Cambridgeshire). From "Chapter 12, Nicknames from Physical Characteristics" in P.H. Reaney's book "The Origin of English Surnames", ISBN 0 7100 2885 7 (c).