Well, the cheapest way to explore Ladakh is using public transportation. All you need is more time as at most of the places that you'll travel to using buses will take at least 1 night stay e.g. 1 night in Nubra Valley, 1 night in Spangmik near Pangong Tso, 1 night in Tso Moriri. Besides transportation, if you use chadar tents for night stays then cost goes down further as these shared tents will cost you just 200-300 bucks per night. A little costly yet affordable budget option is using shared taxis for transportation but that again is time taking as the taxi owner will wait until it gets full with passengers whereas same is not the case with buses. Hope this helps.