If you really want to drive your own car and your objective is "ease":
http://www.k-a-s.com/

They offer a premium service where you drop your car at the airport - then they drive it to a parking lot across the bridge on the mainland - and make sure its back at the airport for you on your return date.

Another option would be to do a one-way car rental - drop the car off at the rental spot in front of the Aero Plaza at KIX and then walk across the bridge to the terminal. (I have done this once - and it's remarkable how close the rental locations are to the terminal. No messing around with bus connections from rental company lots etc.)

But even with these options, I can't think of many situations where I would prefer to drive to KIX. If I had a lot of luggage, I'd be inclined to go with the Takkyubin option that Ksandness mentioned...