I am not tracing the Ridgeway name but thought you might be interested in the following who ran pubs in Rotherham.
Elizabeth Ridgeway 1822-1824 Black Bull
George Ridgeway 1839-1846 Bridge Inn
Ann Ridgeway 1847-1854 Bridge Inn
Mathew Ridgeway 1871-1877 Foresters Arms

Regards, John http://www.rotherhampubs.f9.co.uk