I wonder about that given Idaho's definition of "hunting".
"Hunting" means chasing, driving, flushing, attracting, pursuing, worrying, following after or on the trail of, shooting at, stalking, or lying in wait for, any wildlife whether or not such wildlife is then or subsequently captured, killed, taken, or wounded. Such term does not include stalking, attracting, searching for, or lying in wait for, any wildlife by an unarmed person solely for the purpose of watching wildlife or taking pictures thereof."
You did not "hunt" on private land according to your story and this definition. You hiked/rode your bike on private land. The definition above does not seem to include any verbiage about "packing" game meat or other parts.
You should have only been cited for trespassing, not trespassing while hunting. A first offense for that type of trespassing is an infraction punishable by fine of $300.
Although not your situation, I would argue that a person is trespassing while hunting if you were on your way in to hunt and passed through private land, because you are "pursuing" wildlife at that point.