It now seems to come under Falkirk rather than Denny so I'm a bit confused as to where it actually is/was as I thought Denny & Falkirk both came under Stirling 
Thanks to a reorganisation of local government in 1975, the present local authority boundaries are largely irrelevant for historical research, except that archives now tend to be held according to the newfangled boundaries.
Also, you need to be quite clear when you are referring to the County and when you are referring to the parish. Parishes are mutually exclusive, that means that a place cannot be in more than one parish, though this can be confused by boundary adjustments over time, and there are some places with the same names in adjacent parishes. Also, some parishes are partly in one county and partly in another.
For purposes of genealogical research, the parish is the basis on which information was usually recorded.
The Burgh of Stirling is mostly in the parish of Stirling in the County of Stirling (also known as Stirlingshire but
never as 'County Stirling' or 'Stirling County') but the town expanded into the adjacent parish of St Ninians.
The parish of Denny is in the County of Stirling.
Bonnybridge is a village in the parish of Falkirk in the County of Stirling.
For lots of useful information about what is where, explore
http://www.genuki.org.uk/big/sct/STI/index.htmlMaps used to show the parish boundaries, but the current ones don't. You can view older maps with parish boundaries at
http://maps.nls.uk/index.html, or you can buy second-hand copies of the old one-inch-to-the-mile maps, which also show parish boundaries.
Since 1975 the County of Stirling ceased to be an administrative area, though it continues to exist as a historic and ceremonial county. It was mostly split between Stirling District and Falkirk District. Bonnybridge will be in Falkirk District, and I expect Denny probably is too.