I am trying to figure out a schedule to visit, Shaolin Temple, White Horse Temple and Longmen Grotto

Yes, the Shaolin Temple is a little far from the other two. The White Horse Temple is around 16mi from the grottoes. Generally, a whole afternoon is enough for the latter two attractions. However, the Grottoes is worthwhile an afternoon to enjoy and the night view there is also very nice. Well then, I would suggest you go to White Horse Temple in the next morning and then head for Shaolin.

I cannot exactly figure out your questions by the list. But I can tell you that the direct tourist buses to Shaolin can be taken at LY Railway Station (suppose you will arrive at this train station from Xian). It takes around 2 hours. Local bus no. 56 can take you from LY Train Station to White Horse Temple and the duration is around 50min. Bus no. 81 from the train staton to the grottoes takes around 70min.

Thanks for your advice.

Is there a direct bus from the White Horse Temple to Shaolin?

No, there is no direct public transportation from White Horse Temple to Shaolin. So take a taxi or use local bus no. 56 back to LY Railway Station first. Then you can catch a direct bus to Shaolin near the train station.