Transportation in Israel
From the Givat Haviva you can get to almost anywhere in the country by bus, but there’s also a train and small shuttles called sheruts. To find a bus schedule, use the Egged website and click on “Plan a trip” and then type in your starting point and destination. The easiest place to travel from is Karkur Junction, which will take you to Tel Aviv and Jerusalem. You will be introduced to this stop and others in the area upon arrival. In addition, there is a bus from Barkai to Hadera every few hours. From Hadera you can find busses to Tel Aviv, Haifa and other cities.
The closest train stations are in Binyamina and Pardes Hanna. The train stops at many locations in Tel Aviv including the university and the airport. A taxi from Barkai to the train station should cost 50-70 NIS (more on Shabbat).
From Tel Aviv to Givat Haviva there are public taxis (sherut shuttles). You can get on one at the Tel Aviv central bus station and look for the sherut to Afula/Nazareth (Shabbat as well). The sherut will drop you off close to Givat Haviva (20 min walk) at the Karkur Junction.
Websites to Help You:
General Transportation Information
Aggregated Bus Information
Egged Bus Company
Dan Bus Company
Taxi Company that Will Pick up From Givat Haviva
Please note that in Israel public Transportation generally ends two hours before Shabbat and starts again one hour after Shabbat.