The Negev is not the empty wasteland it appears to be from a plane. From roughly the third century BC to the second century AD, the Nabataeans, a people of Arabian origin who made their capital at Petra, ran one of the most profitable trades in the ancient world through it, carrying frankincense and myrrh from southern Arabia to the Mediterranean ports of Gaza. They controlled the water, building cisterns, dams and terraced fields to farm in an area with almost no rain, and along the route they raised caravan stations, forts and small cities, among them Avdat, Haluza, Mamshit and Shivta, which UNESCO listed together in 2005 as the Incense Route Desert Cities.
Spring brings a thin green, and after rain, flash floods can thunder down the wadis with no warning, so keep out of dry channels if clouds are around. Summer midday temperatures are brutal, and winter nights can be cold, so the best months for riding are March, April, October and November.
The riding is among the most atmospheric in the Middle East. Long, wide roads cross empty plateaus and drop in switchbacks into the deep valleys, with views over the crater of Makhtesh Ramon, the largest erosion crater in the world, near Mitzpe Ramon. Expect strong crosswinds on exposed stretches, and watch for camels and ibex wandering onto the road at dusk. Gravel on the shoulders can be treacherous.
Fuel is the practical question. The desert has long gaps between towns, and Mitzpe Ramon, a small town of a few thousand people on the crater's rim, is the reliable stop, so top up there, and carry water. Check the current security situation and military zones before heading off the main roads, since parts of the Negev contain firing ranges and border areas.
Stand still for a few minutes in the evening when the sun drops and the chalk goes pink, and the silence of the desert will tell you more about the old trade than any sign.