According to Google Maps, the trip from Kathmandu to Leh would be a grueling 16 hours by air, twice that by car. I do not know what route they are taking, but a dedicated group described as "Kung Fu Nuns" is currently completing this journey by BICYCLE.
As someone with very minimal biking capabilities, I have tremendous respect for these women, 500 of whom trekked 4,000 kilometers to draw attention to the worldwide problem of human trafficking. That is well over one million nun-miles in some of the world's most serious hill country!
Nita Bhalla tells their story in Business Insider.