The drive from Keflavík airport is aproxmately 40 min. The driver will be waiting for you with your name as soon as you enter the public arrival hall. It saves you a lot of hustle since the buses cannot drive you directly to the final destination.
It is an ideal to use this trip to stop in the Blue Lagoon on your way to Reykjavík and the driver will wait you and drop you off at your final destination. Including the Blue Lagoon the additional price for the the stopping depends of the time spent in the Lagoon.
The prices you may see on the right side.
Keep in mind that the Blue Lagoon does not open until 8 am in the winter time so it might be ideal to stop on your way back home if you arrive with a early flight.