If you don't have any luck with Bucks Archives, you might want to consider this person:
Sarah Bettles baptism at Uxbridge 25 May 1828 d/o Thomas and Harriet
address: Hillingdon
father's occupation: shoemaker
Thomas and Harriet also have a daughter Maria baptised at Uxbridge in 6 January 1822.
1841 census has a Thomas Bettles (Ancestry transcribes as 'Bettler') shoemaker aged 40 living in Langley Marish, Buckinghamshire. With him are Maria aged 20 and Sarah aged 14. None are born in Buckinghamshire.
In 1851 I can only find Maria, who married John Beacham (transcribed 'Bentcham').
Probably not the same Sarah Bettles, in 1861, in Langley Marish there is a Sarah Bettles (transcribed 'Bittles') aged 30, widow born Wexham, Buckinghamshire.
With her is Henry Bettles, nephew, aged 10, born Staines, Middlesex.
The GRO index does not show a Henry Bettles registered in Staines district for 1850/51. However there is a Henry Charles Bettles registered in Clerkenwell district March quarter 1851, no mother's maiden name given, which would mean that she was unmarried.
Sarah Bettles aged 31 d/o Thomas Bettles, shoemaker married William George Beech in Fulham 23 January 1860.
This couple appear in Fulham in 1861. Sarah Beech's birthplace is Uxbridge.
In 1871 the Beech family are in Paddington. With them is Henry C Bettles, nephew, aged 19, born in Staines, Middlesex.
Henry Charles Bettles married Mary Ann Styles in Paddington 24 August 1873. He names his father as Thomas Bettles, shoemaker (it isn't unusual for an illegitimate child to name their maternal grandfather as their father in the marriage register).