Does the bare wire in an 8/2 cable connect to neutral or ground at my sub-panel?
The current National Electrical Code that most jurisdictions employ will no longer allow a 3 wire sub-panel feed.
4 wire feeders are now required for sub panels. Two hot legs, a neutral, and an equipment ground.

250.32 Buildings or Structures Supplied by a Feeder(s) or Branch Circuit(s).
(B) Grounded Systems.
(1) Supplied by a Feeder or Branch Circuit. An equipment grounding conductor, as described in 250.118, shall be run with the supply conductors and be connected to the building or structure disconnecting means and to the grounding electrode(s). The equipment grounding conductor shall be used for grounding or bonding of equipment, structures, or frames required to be grounded or bonded. The equipment grounding conductor shall be sized in accordance with 250.122. Any installed grounded conductor shall not be connected to the equipment grounding conductor or to the grounding electrode(s).

Hopefully, you can correct this without too much hassle.
Good luck!