Where do I put the ground wire coming from the switch to the new bathroom fan?

Connect it to the ground screw, ground clip or ground wire in the fan.
Not knowing which fan you have or any other information about this installation that is the best I can do.

I agree but lets be clear. You have a black hot wire coming to the switch and then that black continues from the other switch terminal to your fan. You also have aground screw (green) on the switch?

I suspect that you have a black conductor from the switch to the fan. You most likely have a reidentified White (marked with black ink or tape) going from the black wire in the ceiling to the switch.

The bare copper wire will connect to the green screw on the switch and then to the bare copper conductors in the fixture's box.

If you could please attach a photo of the fixture's box we could stop guessing and give you a better answer.