Security officials said the source of yesterday's explosion was not clear, but they believe it was either a car bomb or a roadside bomb that was detonated by remote control.
Almost all 33 passengers on the bus were wounded by the explosion and were being treated in hospitals in Egypt and across the border in the Israeli port city of Eilat.
The bus had arrived at the Taba crossing from the ancient Greek Orthodox monastery of St Catherine's in central Sinai.
The attack came as defence lawyers for ousted Egyptian leader Mohammed Morsi and other defendants walked out of court to protest at the soundproof glass cage in which defendants are placed.
A recess was ordered after the lawyers left Sunday's hearing, the first in a case in which Mr Morsi and 35 others are facing charges of conspiring with foreign groups and undermining national security.
The cage was introduced after Mr Morsi and his co-defendants interrupted the proceedings of other court cases by talking over the judge and chanting slogans.
It is fitted to give the judge control over whether the defendants can be heard or not. Mr Morsi was ousted by the military following million-strong protests after just one year in power.