Bus service Amman-Israel

There's a bus that leave from the Airport to Amman then from the north bus station there's a shared taxi to King hussien bridge, But if there will be others it will be better to share a Taxi and It should cost around 35 JD per car .

As indicated you need to leave Queen Alia to Amman first and leave for the border from the capital city.
Except if you use a contracted taxi from QA to the border (King Hussein Bridge) but the price will not be the same...

Michel

Why don't you fly directly to Israel if you leave Jordan as soon as you arrive at Queen Alia ?

Michel

Thanks
Its much cheaper to go to Jordan.
Do you know if I can cross in this bridge with an Israeli passport?

There is a peace agreement since a long time between Israel and Jordan.
It's not a problem to cross the border between the two countries even (...) if you have an Israeli passport.

Michel

You will not be able to cross the King hussien bridge with Israeli passport but from the northen one Sheikh Hussein bridge or south border to Aqaba with Eilat .

@mvbergen I wouldn't be so sure about Israeli passports allowing entry through King Hussein bridge. Wikipedia states: "Israeli citizens are not permitted to use the terminal", however it fails to explicitly clarify if this statement is valid for travel from west to east only (as some sources like this one mention ), or also from east to west. Another source mentions Israeli passport holders "are prohibited from using the Allenby Bridge-King Hussein crossing, unless as part of an official delegation or with special permission from the Israeli authorities."

Let me suggest the original poster gets in touch with their embassy to know the exact requirements and any possible restrictions. I guess the trip from King Hussein bridge to Sheikh Hussein bridge would be an expensive one by taxi.

Last but not least, note the opening hours of King Hussein bridge. You need to factor that in when you are planning to use public transport or shared taxis. If you arrive there too late, you will have to wait till the next day.

@6 Cleopetra is correct:
Rabin (Arava) crossing point - This crossing point between Israel and Jordan is intended for Israeli citizens and foreigners. Border crossing services are provided Sunday-Thursday 06:30-20:00, and Friday-Saturday 08:00-20:00.

Jordan River crossing point (Sheikh Hussein) - This crossing point between Israel and Jordan is intended for Israeli citizens and for foreigners. The crossing point is open seven days a week 06:30-22:30. Border control services are provided during all the hours of the crossing point's activity.

Source: http://mfa.gov.il/MFA/ConsularServices/Pages/Crossing_points.aspx

Sorry.
I didn't cross it myself and in my mind I was thinking that it was possible.

Michel