Longmen Grottoes and Shaolin Temple

If you join a tour of some tour agency, the time is enough. If you travel on your own, it may be a little bit tight.

You will reach LY Railway Station. right?
If so, outside railway station, you can find a long-distance bus station, where you can find direct buses for Shaolin Temple. After that you need to go back to the LY railway station and take local public bus line K81 to reach the Longmen Grottoes. After visiting, take a taxi to the Longmen Station.

The bus line 33 costs about 1RMB per person and the bus line costs around 1.5RMB. The bus fare from LY to the temple costs around 20 to 30RMB per person.

Thank you... I would like you to tell me whether this plan is OK or not:
-as soon as I get to Luoyang, take the bus to Shaolin.
-visit the place.
-after visiting Shaolin, take a one-way taxi to Longmen.
-after visiting, come back to Luoyang.
What do you think? Are there taxis at Shaolin? And how much approx. would cost that taxi?
Thank you very much.

The taxis can be easily found outside Shaolin Temple, but it may be hard for you to take one to LY, because the distance between the two cities is so far. I heard once one person take a taxi and cost around 600RMB to back to LY.

For your case, you can join a one day tour for the two places and tell them that you will not need a tour guide, so that the price will not be so high. As I know, this website provide such kind of service and you can fill a form in the "Tailor Made Your Itinerary" section and they will tell you the price and the routes.