In 1895 the proprietor of the Bridgehill Inn was Dan. Stewart, hotel keeper, South Queensferry, occupier John Ponton
In 1905 John Ponton was proprietor and occupier.
14 October 1903 Newspaper: Falkirk Herald
has, under Stirlingshire, new license applications,
new premisesJohn Wilson, grocer, Avonbridge, Slamannan, Public-House, Applicant & Proprietor
Then in November the same year he was fined for selling watered-down whisky, so it seems he did get the license.
At this time John Ponton was definitely at the Bridgehill Inn, so I think we can rule that establishment out, if the John Wilson connection is a firm one.