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This website provides several transportation options for your outbound trip and a shuttle for the return journey:
33 minutes, Β£2. This takes 30 minutes and it takes you Tirana which is a 3 minutes walk from the square. The last bus is at 23:00 and the first one at 08:00, which works for your inbound flight but not your outbound one:
There is a shuttle for Β£3, with the last one arrivant at 0:30. I assume this will be enough time for you (2 hours before your flight):