Hi there,
NSW ER 1870 CARCOAR (a different electorate from BATHURST

)
John Cashen, residence, King’s Plains.
NSW ER 1878 CARCOAR
Henry CASHEN, King’s Plains, residence, near Blayney
Thomas CASHEN, King’s Plains, residence, near Blayney
Edward CASHEN, King’s Plains, residence, King’s Plains
James CASHEN, King’s Plains, residence, King’s Plains
John CASHEN, King’s Plains, residence, King’s Plains
NB, I have checked both the NSW ER 1870 and the 1878 BATHURST rolls, and there’s not a CASHEN (or variations) to be seen anywhere near BATHURST

.
I know where King’s Plains are, but as I was born and raised in the central west, I am surprised your local family history meeting refers to Kings Plains area as ‘around Bathurst” rather than as being around Carcoar. In the 19th Century, Carcoar was quite a leading place to be, you are searching for 19th Century sightings surely
So, perhaps your enquirer may be interested in searching some of the 19th century electoral rolls? These are available via NSW SL and some are also at NSW SRO.
Cheers, JM