what is the best way to travel from Lijiang to Shangri-la? and how to get to snow mountain

To Shangri-la, you can take long-distance bus at LJ Bus Station, There are many schedules every day that can take you to the destination. The operating hours are from 07:30 to 17:00. The ticket fare is CNY 63. And it takes around 4 hours on the way.
To the snow mountain from the city, you are suggested to hire a private car. The fare is CNY 500 to 600 for the round trip.

Hearty thanks, Gloria for your kind and quick info

The distance to Shangri-la is about 187 kilometers, there are 3 - 5 scheduled buses from 7:00 - 15:00 every day. The fee is RMB 45.

thanks so much, NEHOW, for your kind and valuable update