The airport transfer in Menorca can be quite expensive if you choose options such as taxi or uber. But the trick to do it very cheaply is to use the bus.
The company that runs the bus in Menorca is called "Torres". https://www.bus.e-torres.net/en/lineas-regulares/route-10/
to the bus station in Mahón, from where you can travel to most of the tourist centres and towns on the island.
The airport bus stop is located on Arrivals level 0.
Route 10 is the bus that travels between the airport and the bus station and costs €2,60.
From 1 June to 30 September:
To Mahón (bus station): From 5:55 to 23:25.
To the airport: from 5:45 to 23:15.
Frequency: Every half hour.
From 1 October to 30 May:
To Mahón (bus station): From 5:55 to 22:15.
To Airport: From 5:45 to 19:45.
Frequency: Every half hour.