Do you think there would be a church or somewhere in Bannockburn I could stop into and see if they have a record?
Quite honestly, no, I do not think so. Any records from the late 17th century are very unlikely still to be in the church, even if they have survived. I am willing to bet that stopping in to any existing church, anywhere, not just in Bannockburn, is almost certain to be a complete waste of time as far as seeing older baptism records is concerned.
There seem to be three main churches in Bannockburn.
One is the Allan Church of Scotland. All the registers of the Church of Scotland were transferred to the Registrar General for Scotland in 1855, and they are now indexed on Scotland's People. The Allan C of S web site says it started serving its community in 1838. Originally it was probably a chapel of ease or quoad sacra parish set up withing the parish of St Ninians.
Then there is Our Lady and St Ninian's, which is Roman Catholic. All the Roman Catholic registers are available through Scotland's People.
Lastly Ladywell Church of Scotland, which from its web site looks very new. In any case it too is part of the C of S so will not have any older registers.
Any church other than the Church of Scotland, Roman Catholic or Episcopal Church of Scotland, such as the Christadelphian Church (founded 1838) and United Free Church (formed in 1900 by the union of the Free Church of Scotland (founded 1843) and United Presbyterian Church (founded 1847 by the union of the United Secession Church (founded 1820) and the Relief Church (founded 1761))) did not exist in 1682.
If you want to see pre-1855 baptisms, the place to go is the Scotland's People Centre in Edinburgh.