Bribery ? Such ugly word. I think you mean generous financial aid on infrastructure development
Let's look at it geographically.
You have Israel and Palestine.
To finally achieve the two-state solution we're talking about here, all of Palestine's Arab allies must recognize Israel.
Bush got Egypt in 1974, this leaves out
01.
Lebanon - In a devastating multi-sided civil war. We don't know who the de facto ruler of the country is.
02.
United Arab Republic - Ruled by Saddam Hussein, who hates Israel. I don't think any form of negotiation is possible with him.
03.
Saudi Arabia - Firmly against Israel, and with US influence at an all-time low, I can't see any form of bribery working. Add to that Mecca and Medina. Controlling the holy cities has always given any Islamic nation extra clout, and other Muslim nations are going to listen.
04.
Yemeni Arab Republic (North Yemen) - Established in its current form in the 1950s, it is a Nasser-style Arab nationalist government. Generous foreign aid against South Yemen may work here.
05.
People's Democratic Republic of Yemen (South Yemen) - The only communist country in the Middle East, they are firmly under Soviet influence, with very poor relations with the rest of the Middle East. North Yemen may be nudged into recognizing Israel by funding its army against this nation.
06.
Oman - Western-sympathetic monarchy. May be easily swayed.
07.
United Arab Emirates - Western-sympathetic monarchy. May be easily swayed.
08.
Qatar - Western-sympathetic monarchy. May be easily swayed.
09.
Bahrain - Western-sympathetic monarchy. May be easily swayed.
10.
Kuwait - Western-sympathetic monarchy. May be easily swayed.
11.
Libya - Read the UAR, the good Colonel will be very unwilling to negotiate.
12.
Jordan - Western-sympathetic monarchy. Will be easily swayed. The PLO taking refuge in Jordan almost got the country into civil war.
As of right now, even ITTL, is an Arab issue rather than an Islamic one.
RFK and Edmund Muskie have a hell of a job cut out for them.