Note: Here’s an update from May 2019: Taking the Bus to Tirana’s Airport. The information below is no longer accurate.
It is possible to take a bus to Tirana’s airport, but unfortunately the service hasn’t got a web presence. The bus service is called Rinas Express, and operates every day between 7:00 and 19:00. It leaves on the hour every hour, both from the airport and from the town centre. It costs 250 Lek for a ride, which takes around 25 to 30 minutes. You buy the ticket in the bus (once it’s ready to depart; just sit in if you arrive earlier).
Finding the bus can be a bit trickier. At the airport, you simply walk straight on (don’t turn right towards the taxis when you leave the terminal building). In town, head to Skanderbeg Square, more specifically the National Museum. Rinas Express departs slightly off the square at the beginning of Rruga e Durrësit.
Or just get a taxi…