If by ‘around’ you mean ‘without driving’, it’s either Muiravonside or Beecraigs.
But if ‘around’ includes a car, then no need to head anywhere near Glasgow … you are 20 min drive from Stirling, which’s got some of the best trails in central Scotland both north (e.g., Ochills) and south (Cambusbarron, etc.), the Stirling Bike Club does regular rides around there.
For trail centers Carron Valley is about 20min drive (though IMO much better riding to be had around Stirling for the same drive). There is also Comrie Croft, which is under an hour from Falkirk and is worth an afternoon visit.