Dear Jake,
Shalom. Thank you for writing us.
On Saturday, public forms of transportation do not work in most parts of the country. However, you do have taxis. That would be no problem and the taxi can take you to Tel Aviv or other parts of the country. Please be advised that during April, the 8th of April is Passover eve and most businesses and transportation work half day, the 9th is a holiday and everything is closed for holiday except national parks, the same is true for the 14th and 15th of April; Fridays are also short days; Israel's Independence Day is on April 29th. On the upside, during this period there are many events and festivals for domestic tourists as well as for those from overseas.
May 1 is a normal day here. You can check into a hostel on Saturday providing you make arrangements in advance. Please check out the Israel Youth Hostel Association website: http://www.iyha.org.il/eng/
We hope you enjoy your visit,
All the best, Nancy Shedlaz, Israel Ministry of Tourism