We are not renting a car bc we are going to argentina one day (and driving a rental in argentina gets tricky), and we are going to be near our hotel on another day. The airport is a few minutes walk from the hotel as well.
So we figured we are not renting a car for one day and having to worry about parking, etc.
Of course this could all change in a few days. We still have a good 55 days till vacation.
Anyway, this is a good site:
http://www.clickfozdoiguacu.com.br/ - it gives you some information on public transportation at the very bottom of the page.
and so is this:
which give you the address to the bus terminal and their phone number.