Quote Originally Posted by markb
Just use graphite or nut sauce on the nut. The bigsby's moving parts run on delrin bushings which are effectively self lubricating. I'd only lube the roller bridge if it starts making squeaks or pings that you can hear through an amp. A drop of light oil on a toothpick applied to the roller axles would be the way to go here but use it sparingly and wipe up any excess. Don't get machine oil on the guitar's finish.
One adult among the whole bunch.:

Shiner has a lot of competition with the responses that were posted.