Of the three names below Bastard most obviously originated in a nickname. As might be expected, it was found over a wide area in the 1500s.
Bariball probably developed from the name Barbarel, introduced by the Normans and present in the 1300s in Devon, where it’s been suggested it was from a nickname. Or did it come from the first name Barbara?
The most obscure is Basher. Only two examples are found in the 1500s, and these widely seperated. There is also a possible Annis Bashe at Sancreed in West Penwith in 1582 although the reading is unclear. To deepen the mystery further it then disappears for over a century before popping up again on the Lizard.
You can find maps of these names in 1861 for comparison here.
Cornish studies resources 
I checked the meaning of Bashe and it comes up as a Hebrew name. As a first name it means Daughter of God but it can also be a surname and was used as such by Russian emigrants to the USA at the end of the C19. It is very plausible to have a Jewish population, potentially including immigrants from overseas, in Cornwall I think. It also seems plausible that new immigrants with the same name but no knowledge of earlier Bashes a century before could have arrived. If only first names were used then Bashe could refer to women only.
I did a quick dive into Bastard and learned that it did not have negative connotations for many centuries. Apparently it arrived with William the Conqueror, himself known as William the Bastard, and this name was associated with natural offspring from noble families. https://www.surnamedb.com/Surname/Bastard
Another comment from the net – Middle English: via Old French from medieval Latin bastardus, probably from bastum ‘packsaddle’; compare with Old French fils de bast, ‘packsaddle son’ (i.e. the son of a mule driver who uses a packsaddle for a pillow and is gone by morning).
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