It might take you around 3 hours to reach Shaolin from Longmen, since you'll have to take bus to Luoyang Railway Station and then take long distance bus to Shaolin Temple after visiting Longmen Grottoes. Is your oroute Xian-Luoyang-Beijing? If so, you can take highspeed train from Xian to Longmen Grottoes firstly in 2 hours, and then take bus to Shaolin Temple. Finally, take a bus from Shaolin Temple to Zhengzhou City, where you can take bullet train from Zhengzhou to Beijing directly in 5 hours, you can check China Tours(https://www.travelchinaguide.com/tour/default.htm) for more details about the itineraries.

We plan to stay in Xian 2 days. First day we go to Louyang for Longmen and Shaolin, and last day visiting terracotta and city wall in Xian. By night, day 2, we'll fly to Beijing. My question is can we manage the travel from longmen to shaolin easily by relying on shuttle bus and train schedule? How much longmen-shaolin bus will cost?