Carol
We lived on Kefalonia for nearly eight years and I can honestly say that the buses there ran meticulously to time. The one and only time when we had a problem was the time that a forest fire had spread across the main road and had prevented the morning bus from arriving. This is not the sort of record that I would call "extremely unreliable". I can't speak about Corfu buses from personal experience, but I would be surprised if they operated any differently.
We used to get very annoyed when we repeatedly heard the tour company reps tell their guests at the welcome parties that the buses were very unreliable and you may find that you arrive somewhere by bus but can't get home again because the return bus doesn't turn up. This just wasn't true and they only said it to stop guests using the buses, so they would buy more excursion tickets or a rental car from them instead.
The other problem was that the same guests would repeat this to their families when they got home, helping to create a dreadful myth that Greek buses were rubbish.
There is a web link to the bus timetables for Corfu here:
http://www.allcorfu.com/ou-buses.htmlThis shows that there is a bus from Arillas to Corfu Town at about 06:45 and a return one leaves Corfu Town bus station at 13:45. It doesn't say how long the journey is but, judging from the timings, it may be up to 90 minutes, so take some water with you and have a snooze on the way.
Good luck
Stuart