normally, getting from Israel to Cairo shouldn't be a problem. As long as you don't have a 4x4 you can cross the Taba border (we just did it, albeit the other way round from Egypt to Israel) and had absolutely no problem.
Zhen you can ride from Taba via Sinai (probably have to go the long way round, i.e. through Dahab, Sharm, El Tur) and through the Suez tunnel to Cairo. Worst case is, they will make you go in a convoi (mostly between Dahab and Sharm, we didn't have one but we heard from others who were made to wait at the checkpoint).
As I said before, we did it the other way round: we went from Cairo to Sinai, stayed at Dahab for a while and then crossed into Israel with two motorbikes. we didn't have any trouble.
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