I have a gretsch with a bigsby, and a few days ago I used the bigsby (I've used it many times before) and I hear a clicking like noise, but no strings are snapped, despite me being fairly gentle with the bigsby. The high E string sounds fine when you play it open, but if you try to play a note it doesn't actually make a normal sound, it almost sounds as if you were plucking the strings above the nut. The B string registers a note when open and played but it's buzzed above fret 6, all the other strings are fine. I can't seem to track down the problem either, could anyone spare some advice?
Since the Bigsby operates behind the bridge, whilst it may be the cause of the problem, it won't be the cause of the noises, or strings binding.
The strings only vibrate between fretted point and saddle. So the problem is either the saddle itself or the string catching on frets in between. Check the bridge/saddles and also sight along the neck, which may not be as straight as it was. Using the Bigsby alters the string tension, both ways, and that could have affected the contour of the neck, thus the fingerboard. Sounds like it's find a luthier time.
Or, you may be lucky, and can raise the bridge - I suspect just on that side, so the action is higher for the top 3 strings.