Hi Emma,
Taxis in Israel are safe for women. As a woman myself I feel more comfortable sitting in the back rather than next to the driver, but you have nothing to worry about.
There is unfortunately no public transport to Beit Guvrin. If you want to save some money, you can take a bus from Jerusalem to Beit Shemesh (details follow) and a taxi from there.
I assume you need to be at Beit Guvrin very early. The first bus, route 415, leaves from platform 2 or 3 in the Jerusalem central bus station at 6 a.m. and takes exactly 29 minutes to the first stop in Beit Shemesh. The one after that is at 6:40 a.m. The bus fare is NIS 11:30 in each direction (there are no return/round-trip tickets). Buy your ticket on the bus. Get off at the first stop in Beit Shemesh (which is a medium-sized town). Landmarks to look out for: the bus crosses railway tracks (a level crossing if you speak British!) and then turns left. There is a McDonald's (!) there. Ring the bell when you see all these things! A big sign will tell you that you are in Beit Shemesh. Get off the bus there.
Now, chances of finding a taxi there at 6:30 a.m. are pretty remote. I suggest you call one of these local Beit Shemesh taxi companies the evening before and arrange to have a cab meet you there. Tell them that you will be at the bus stop opposite BIG (that is the name of the shopping mall where McDonald's is) having come from Jerusalem. Everyone in Beit Shemesh knows BIG (pronounced as the English word, not initials).
Carlos Taxis tel. 999-3333; Sharett Taxis tel. 999-7777, Shemesh Harama Taxis, 999-9999. Area code is (02) if you are calling from outside Jerusalem (Beit Shemesh is within the Jerusalem area code, so if you call from Jerusalem it's without the 02). (If you are using a foreign cellphone, it's +972 2 999-xxxx.)
When you finish for the day, if you can't get a lift from someone on the dig, call one of those companies and arrange to have a cab take you from Beit Guvrin to the bus stop at BIG in the direction of Jerusalem. Beit Guvrin is outside the 02 area so you will need to dial 02 if it's from a payphone. Buses leave Beit Shemesh for Jerusalem every half hour at xx:00 and xx:30, and take about 22 minutes to get to that stop. Note that several routes stop there, but the only bus that will take you back to Jerusalem is the 415.
The 415 bus is operated by Superbus, not Egged, so you won't find it on the Egged web site.
If you need any more info on this send me a PM (private message).
Enjoy the dig. I wish I was going too!
