Check out this link.
http://millertransportation.com/tours/casino-tours/
Miller offers a shuttle bus (for $20, and they give you a free $12 food voucher, and a $5 casino chip) if you get to Louisville early in the morning. That is what I will be doing next week, because I do not have a car. You would need to take the #2 Louisville TARC bus from the airport, and ask the bus driver what bus you need to transfer to from downtown in order to get to one of the locations that the casino shuttle leaves from. You will need to arrive at the airport by 7 am I am guessing, or you may need to take a cab to get to one of the locations listed in the link above. Maps.google.com can give you great bus directions. I am taking the one that leaves the Steak N Shake on Dixie highway at 8:50 am. If you can't get there early enough, then the TARC bus can get you as far as New Albany Indiana (which is about 9 miles away from the Casino, and I imagine a taxi from there might be around $20, but not sure).