Traveling from Riyadh to Jordan to Jerusalem

My family and I would like to go on tour from Riyadh to Jordan to Jerusalem for about a week.
What would be the best way to go about doing this considering all the red tape attached?
I do know that our passports should not be stamped in Israel, we need to get back to Riyadh!!
Could we perhaps fly from Riyadh to Jordan and then go by bus into Jerusalem?
Any advice would be highly appreciated!!!

Hi. This maybe late but i hope this would help.
You can ride a bus going to Jordan then Jordan to Jerusalem. Or if you want a comfy life then you can ride the plane as what you originally planned. Once you reached Jordan, people know exactly what to do so you can go to jerusalem and be back to riyadh. best of luck for your travels. i wanna know if you did it well.

At one time any hint of links with Israel meant no admittance to any Arab states - certainly when i lived in Bahrain in the 90's I used to go into book shops and open an  atlas for eg, and the page with Israel would be torn out of black-marked out! So be careful!! MAKE SURE NO STAMP IN PASSPORT OR YOU WILL PROBABLY NOT BE LET BACK INTO SAUDI!!!  (Israel customs are used to stamping a removable piece of paper though - make sure they do!!)

Make sure you make the most of Jordan! And there is lots to see in Egypt -  going to Israel does seem a bit of a risk (ask your consular section what the feeling is about that!!!) - however I can see the attraction to Israel- it's formation and continuance is really nothing short of a miracle.