I don't know what kind or type of GFCI box you have, but if it has a breaker in it, I would consider this: run a neutral wire from the house to it.
You don't need a neutral wire to run your tub. But if you have room in your GFCI box for additional breakers, you will want to have a neutral wire so you can, in fact, use that capability in the future. For example, if you have a basic sub panel to shich you can add a breaker or two, you can put in an outlet to run good things - perhaps a stereo, a small refrigerator (or towel warmer), bug zapper, some Low Voltage lighting, de-icer for the steps or pathway, hard-wire in some additional lighting. You may never use the capacity, but I assure you, if you
don't allow for it, you'll want it later.
HTH