Schedule for buses around Mytilene town (including buses to Moria and to the airport). Direct link to a PDF file. In Greek only.
Moria schedule is line 15 (weekdays), line 3 (next section, for Saturdays) and line 1 (last section, for Sundays).
English language site for buses across the island. This link goes to the interactive schedule page.
Updated as frequently as possible. Best to subscribe to the UNHCR newsletter to be sure of getting most current details.
City bus app (download for Android, iOS, Windows) is highly recommended.
For buses from Thessaloniki to surrounding towns