Having been there last week (in cold winter), I definitely recommend any traveler to go there with a private car and not try to take a collective tour or public bus in particular if you want to combine it with another site (e.g. Ming tombs).
Indeed, we went the same day to the great wall at mutianyu (north east of Beijing) and the ming tombs (dingling tomb and the sacrdd way, north west of beijing) and did not have so much extra time that day. If you go with a public bus, well you will waste a significant time in the bus and also in finding your way (very few Chinese people have an adequate level of English). If you go with an organized tour, you will likely waste some precious time in a silk / jade / craft factory (for which tour operators get either a commission if you spend a certain amount of time in their shop or a percentage on what you buy should you buy anything!).
Having said that, after a missed tentative to go to the great wall with a tour (in the car they started negotiating on how many factories we should visit and we decided to leave the car), we booked a car via the hotel for a big price (RMB900 for the day).
I can recommend the driver we used who was punctual, polite and understood an adequate level of english and with whom you can have a better price than via the hotel:
LIN YONG - email: LinYongfirstname.lastname@example.org - 13501055560
Visiting the great wall at Mutianyiu was definitely worth it in any case !!!
This review is the subjective opinion of a TripAdvisor member and not of TripAdvisor LLC.