I hurt my tailbone pretty badly last year- I hopped off my bike saddle once but didn't quite make it and came down hard right on the saddle nose with my tailbone. OMG that was some pain.
I had MONTHS where it was hard to sit in any one position for too long. Finally most of the symptoms went away after about 6 months. BUT...I noticed when I sat in certain chairs for a while, when I got up I would feel that awful twinge of pain ABOVE my tailbone just like described here. It always happend when I had been sitting too long in one position and my butt was starting to go numb from the old tailbone incident....then I'd get up and the shooting pain would happen.

I'm thinking your saddle is putting too much pressure in a bad spot and pinching some nerve or blood vessel, and the pain happens when you rise up and blood shoots back in to the area suddenly.