bus service in Sicily

Edwlewis,

I've not traveled to Sicily but thought your might be interested in reading this post by Zoe who travels to Sicily often:
https://community.ricksteves.com/travel-forum/trip-reports/sicily-by-public-transportation

I've found that many Italian bus websites are only in Italian, so I often use google translate to help me figure out the info I need.

Perhaps Zoe will see your post & give you the information you're looking for.

Viamichelin.com gives driving time as nearly four hours, bus will take longer. Would it be possible to fly into Palermo?

The bus schedule at http://www.saisautolinee.it/ is in Italian, but among the most clear examples for Italian bus schedules. Search results are divided for Mon-Fri, Sat, and Sun-Hol and show the whole day.

Or, you can take a 10-minute taxi ride (or local bus) to Catania Centrale train station; direct trains to Palermo take 3 hours and run 6-7 times/day, but only 3 on Sundays. How to Look Up Train Schedules and Routes Online gives you the DB train schedule link and tips for using it.