Bigsby and other vibrato systems can cause tuning problems. Make sure the nut doesn't pinch the strings and lube it, add some locking tuners and the guitar should stay in tune for an entire set.
The Reverend I owned had a Bigsby liscenced B5, rolling Schaller bridge, graphite nut and Sperzel locking tuners. My current Gretsch has an open V B7 Gretsch Bigsby, tune-o-matic bridge on a rosewood base, bone nut and again, Sperzel locking tuners.
Both these guitars stay in tune for more than a set (10-12 songs) unless you go ape with the Bigsby.