Clare,
Ashton is a village or hamlet with no church in the parish of Bishops Waltham. Therefore both Ashton and Bishops Waltham can be considered correct for a place of birth. Have a look at an OS map on:
http://www.streetmap.co.uk
You will see how close the two places are.
Stephen is the only Barnes child born to parents James & Sarah in Bishops Waltham that I can find. I have found a James baptised in Millbrook in 1830.
Nell
Nell
There is another child born to James and Sarah in Bishops Waltham, on the IGI. It is Sarah Eliza Barnes, Baptised 03 SEP 1837.
She is then called Eliza on the census.
James and Sarah are also living in Owslebury in 1881. as is son James and family. So I'm sure this is all the same family for Stephen. Though I do find it strange that James and Sarah moved around a lot.
I am wondering if the Barnes could be a Romany family, as when I was looking for possible parents of James Barnes born 1808 in ringwood. A lot of the Christian names had a Romany feel to them. Ringwood, Romsey and Bishops Waltham had strong links to the Romany comunity.
Clare