Hi,
While Egged does not have a direct bus route from Ben Gurion airport to Safad - it is possible to make this trip using public transportation, depending on the time of day. The Egged website offers two options. The first involves taking a bus from the airport to the central bus station in Tel Aviv and from there taking a direct bus to Safad. The other option is taking a bus from the airport to Hadera and from there another bus to Safad.
There are also taxis and "sherut" taxis which offer shared rides at a reduced cost. More information on airport transportation can be found at: http://www.iaa.gov.il/Rashat/en-US/Airports/BenGurion/InformationforTravelers/TransportationToandFromtheAirport/
Have a safe trip, we're waiting to see you.