Yes, there are 2 buses on a Saturday night via Egged bus line #444: One bus leaves Eilat at 16:30 p.m. and a second one departs at 19:30 p.m.
It is a 5-hour trip; the earlier bus is due to arrive at Jerusalem's Central Bus Station at 21.30 p.m.; the later bus is due to pull in at 00.30 a.m.
Egged is the official bus service in Jerusalem. On their website, you can find bus route changes for Jerusalem. They also have a bus routes map, but it is not complete and not updated. On Answers.com there is an entry for Egged bus lines, including a detailed list of Jerusalem lines and their destinations. See the Related Links for the info. For an unofficial updated map of the most useful bus routes in Jerusalem, see the Related Links.
I presume the questioner is someone entering Israel from the Sinai Desert, via the Taba border crossing. From Taba, you need to get to the Central Bus Station in Eilat -- about a 15-minute drive. There are local buses that run this route and, in addition, taxis within Eilat are a dime a dozen. From the bus station in Eilat, there are buses to Jerusalem -- it's about a 4.5-hour-drive. According to the website of the Egged bus company, there are buses at 7 a.m., 9 a.m., 11 a.m, 13.30 p.m., 16.30 p.m. and 00.30 a.m. It's advisable, though, to call Egged to double-check, at *2800 or 03-6948888 (particularly regarding the 00.30 bus, which might only be in operation during the summer vacation months). To see the schedule (in English) of the Egged bus company, see the Related Link.
On a bus, it's about 3 hours or so once you've crossed the border from Eilat, Israel, to Petra, Jordan.
Yes, you can use your bus pass before 9.30 am on Saturdays and Sundays.
Across the street from the main entrance to the Jerusalem central bus station, on Jaffa street.
Using a bus, in order to get from Jerusalem to Herzliya Pituach:Take the 947 or 950 from the Jerusalem central bus station to the Ra'anana bus terminal.Take route 29 from Ra'anana to Herzliya Pituach.Overall, this should take a bit more than two hours.
About 15 hours.
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