transport from Beijing International Airport to Mutianyu Great Wal (return included)

I will have 13 hours layover in Beijing International Airport. I will arrive on 09 March at 11:45am in Terminal 3. My connecting flight is at 01:05am after 13 hours. I would like to visit Mutianyu Great Wall during layover. My budget is ~$80 for it. Drive/car service for 1 person usually is over $150 to Mutianyu Great Wall. I dont know maybe I should find any trip group to Mutianyu Great Wall on 09 March to join them? any advice?