Hello Winto
She should be living with at least her mother, who's name I don't know and am hoping to learn from the census. Her father, William Harrison, was deceased by the time of her marriage in 1873. So may very well have been dead by the time of the 1871 census.
I believe ancestry allows you to narrow searches by name and birthplaces. And I know that Sarah was in Yorkshire in 1871, but not in Barnsley. Is there any Sarah A. Harrison born in Barnsley, Yorkshire around 1854, but not living in Barnsley in 1871 that you can find?
Thanks
Mike