I'm wiring a subpanel for my hot tub. I know the white wire from the breaker goes to the neutral bar, but does the neutral wire from the hot tub connect to the neutral bar or the neutral terminal on the GFI breaker?

I assume it's a 120 volt pump so both the neutral wire and the black "hot" wire from the pump connect to the GFI breaker itself. The ground wire will connect to the grounding bar. Most GFI breakers will be marked indicating which screw is for the neutral.