TOURS: Most of our fellow passengers were on the first leg of brief, low-budget tours of Egypt. Galilee Tours, which has offices in Jerusalem and New York as well as Tel Aviv and was recommended to us by the Israel Government Tourist Office in New York, is probably the largest and most experienced operator of such tours.

There are no-reservation public buses, but foreigners are well-advised to book with Galilee or one of the other tour operators, who provide informative guides on the bus and assume responsibility for the linkup at the border.

These tours provide an economical and convenient way for visitors to Israel to throw in a side trip to Egypt without having to fend for themselves -- or find a hotel -- in Cairo, the largest city in Africa and one of the most disorganized anywhere.

One four-day, three-night Galilee tour, for example, provides round-trip bus service from Tel Aviv or Jerusalem, hotel and two daily meals in Cairo, and visits to the main Pharaonic and Islamic sights of the Cairo area for $125 in a tourist-class hotel or $169 in a luxury hotel. (For those who begin their journey in Egypt, of course, this entire sequence is reversed and a Cairo booking company handles arrangements for tours to Israel, but given the way things work in Cairo, it's easier to start at the Israeli end.)

In Cairo, travelers who are participating in a tour organized by Galilee are delivered to their hotels, mostly comfortable but modest facilities in hard-to-find neighborhoods.

For those who are using the bus just as transportation and are staying in Cairo on their own, it's essential to have confirmed hotel reservations in the Egyptian capital, preferably in writing. Otherwise, the bus simply drops you off at Tahrir Square, the vast, dismaying main square of downtown Cairo, and you are on your own. There is no central registry of available hotel rooms in Cairo, and hotel facilities are scattered all across the vast metropolitan area, so travelers must know exactly where they want to go before trying to flag down a taxi. REQUIREMENTS: Americans entering Egypt from Israel must have valid Egyptian visas in their passports. Visas cannot be obtained at the border. It's advisable, but no longer required, to buy some Egyptian currency at one of the banks in the border station. In addition, the Israelis levy a departure tax of 23 shekels (about $15). It's a useful way to unload Israeli currency, which cannot be used or exchanged in Egypt. INFORMATION: For more information, contact:

The Israel Government Tourist Office, 350 Fifth Ave., New York, N.Y. 10118, (212) 560-0650.

The Egyptian Government Tourist Office, 630 Fifth Ave., New York, N.Y., 10111, (212) 246-6960.

Galilee Tours, 2112 Broadway, Suite 500, New York, N.Y. 10023, (212) 874-4000. (In Tel Aviv, phone 221-372 or 203-311; in Jerusalem, 246-858.) Emeco Travel, 2 Talaat Harb St., Cairo, Eqypt, phone 747-241 or 747-302.