There are two ways to do it. One requires five conductors, the other requires only four conductors, but also a load center.
So in the first example, you hook up the well as before, then run a third "hot" and a neutral for the convenience outlet. The extra hot needs its own breaker back in the house.
In the second method, you'll run your pump wires to the load center rather than to the pump. You'll also need to run a neutral from the house to the load center. Then run the pump and outlet off different breakers in the load center.
In either case, the ground wire should be grounded locally in the pump house; I think tying it to the well pipe should do it, but you might want a separate ground rod as well. The ground and neutral are kept separate in the pump house.