I did this last year but forgot the bus numbers but I found the following and it all came back to me.
Walk down to the waterfront, and buy a bus ticket to the train station from the newsstand (1 euro), then walk around the corner and up the hill so that you’re standing in front of the old theatre. Wait here for Bus #1. Take this bus to the train station, and get off (the train station is an obvious stop, about 10 minutes ride). At the train station, go inside and buy a ticket from the tobacco shop (not from the newsstand) to the airport (2 euro). Catch Bus #J from in front of the train station to the airport — it takes about 35 minutes. Good luck.