Is this bay window under a soffit overhang, or was there a roof built for it? If the latter, that would be a place to look, in addition to the potential of condensation causing it. Very common on under-insulated bay windows.
To fix it, obviously the first thin would be to identify the root cause and remedy, and then you'll probably need to add a thin layer/veneer of wood over that seat board since it is more than likely damaged beyond repair.