Tupiza is the other way into the salt flat, and the better one: instead of starting at Uyuni you ride south-west across four days of red rock, the Sud Lípez lagoons and the Siloli desert, and reach the salt on the last morning. Tupiza Tours, a long-established local company, sells that crossing in both directions.
They also run the thing Tupiza is otherwise known for — horseback riding through the canyons and cactus country around the Quebrada de Palala and the Valle de los Machos, which is genuine Butch-Cassidy landscape — and, improbably, an annual triathlon.
Three offices, in Tupiza, La Paz and Tarija, each with its own mobile; the Tupiza one is the WhatsApp. The Tarija branch, on +591 70522513, runs wine-country tours, the Campiña Chapaca and day trips to the Laguna de Tajzara.