Here are some places from where you can rent bikes in Leh :-
Leh BIke Rental
Ladakh Wander
Venture Third Pole Bike Rental
PRICES MAY VARY
Royal Enfield 500cc Classic - 2100 INR (8am - 8pm)
Royal Enfield 500cc Standard - 2000 INR (8am - 8pm)
Royal Enfield 411cc (Himalyan)- 2500 INR (8am - 8pm)
Bajaj Avenger/ Vikrant - 1200 INR (8am - 8pm)
BMW GS/GSR 310cc - 3500 INR (8am - 8pm)