stiff neck while riding bike?

You're probably not doing anything wrong - just need to get used to biking outdoors.  It's completely different than spin class.  I find that after a winter of spin class it takes me a few rides to get comfy and adjusted back to my bike outdoors again.  The neck pain is probably just from holding your head up over all of the road bumpiness.  Sounds insignificant, I know, but that might be all it is.  Give it at least another couple bike rides to see if it improves and if it still hurts, maybe get a bike fitting.