there is Flybus
Flybus transfer at arrival:
The Flybus is located right outside the Keflavík International Airport. The bus leaves 35-40 minutes after arrival of each flight. Passengers should keep an eye on the screen in the terminal to see when the bus leaves or ask for information at the Flybus information desk at the arrival hall. The trip to Reykjavík will take approximately 45 minutes and upon request, the bus will stop at Hotel Viking in Hafnarfjörður and at Aktu Taktu in Garðabær.
When reaching Reykjavík our first stop will be the BSÍ Bus Terminal. Free onwards transfers are available to all major hotels, the Youth Hostel, Laugardalur camping area and the domestic airport. For these transfers the driver will ask you to board smaller busses.
Flybus transfer at departure:
In connection with all departing flights from Keflavík International Airport, there are Flybus departure from the BSÍ Bus Terminal.
The day before you intend on leaving Iceland, please ask your hotel lobby to book a Flybus transfer for your journey to the airport.
http://www.airport.is/english/menu/trans…
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also taxis from airport.
http://www.airport.is/english/menu/trans…
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Maybe best to ask the hotel if you can about airport transfers.
pehaps they offer free transfers or could collect you.