As there is limited public transport available to/from Ben-Gurion Airport on weekends, a recommended option from Haifa is to use the Amal Taxi shuttle service.
Booking is required 48 hours in advance, and the shuttle can collect you from your requested location. The shuttle service runs 24/7, and costs 110 shekels.
Amal Taxi: +972-4-8662324
On Fridays, buses run until around 1 hour before sunset. Line 947 travels from Hof HaKarmel Central Station in Haifa to El-Al Junction, and you can then switch to line 5 which travels to Ben-Gurion Airport Terminal 3. Plan your journey on the Egged website.
If you are travelling from Tel Aviv to Ben-Gurion Airport on Saturday, the Hadar taxi service costs 110 NIS during the day and 120 NIS at night. Booking is required 24 hours in advance, and the taxi can collect you from your requested location.
Hadar Taxi: +972-3-9711103