It’s a two hour drive to Villa Romana del Casale from Palermo. I would imagine that there are busses, but they would certainly take even longer. Three plus hours each way would give you barely have enough time to enjoy your time there. If you really want to go, I think that a driver is the reasonable way. And, get there as early as you can, preferably at opening time. It gets uncomfortably crowded later in the day. We had to jostle our way through the crowds, which wasn’t helped by people who insisted on backtracking to repeat some rooms. Worth it for sure, but better earlier and with some patience.