Hi DAL,
Bridge of Allan was in Logie parish - just a few hundred yards from its boundary with Lecropt parish. Logie parish was (until 1891) split across county boundaries into three counties - Strlingshire, Perthshire and Clackmannanshire. Bridge of Allan was in the Stirlingshire part. In 1891, the county and parish boundaries were moved and the whole of the parish fell within Stirlingshire.
For genealogical records, you should find that Logie parish is indexed under Stirlingshire for all dates.
If looking up Logie parish, be careful not to be mislead by the other Logie parishes elsewhere in Scotland. See
viewtopic.php?t=5140 for more information.
All the best,
AndrewP