This website provides several transportation options for your outbound trip and a shuttle for the return journey:
#Bus
Bus
33 minutes, £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:
#Shuttle
Shuttle
There is a shuttle for £3, with the last one arrivant at 0:30. I assume this will be enough time for you (2 hours before your flight):