I am assuming that you also have a light that runs off the same switch.
It sounds to me that if this is the case, you will have to have an electrician run a new feed to the GFI.
currently,if you bypass the switch, your light will probably always stay on.
The wire probably goes from the switch to the GFI and then to the light.
This type of wirering is generally quite old and done with two wire. I would be very surprised if the GFI worked right because it may not be grounded.
Again, another reason for getting an electrician.
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