How do you guys wash your car with hard water?

Ok . . . . my car needs to be washed. Last year it was waxed / polished, maintained. But I've run out of time. I need to wash her. My issue is that I have hard well water. Yes, it is on a water softener, and I have a Whirlpool whole house filter in the system. I am capable of using this conditioned / filtered water outside at my tap by opening / closing a couple of valves. I'm just scared to death to try it. Fear of water spots etc. What do you think?

Rog