what is the best way to travel to Guilin North Railway Station from Yangshuo in the early morning?

Well, you need to take a long distance bus from YS Bus Station to Guilin General Bus Station, which is available from 6:45 to 13:25 and takes CNY22, 90 minutes.
After you get there, you can take a bus no.1, 99 or 100 to North Railway Station, which may take 10 minutes and CNY20-30.

Well, you can also take the bus directly to Guilin North, and the bus leaves at 10:00, 11;30, 14:00 and 16:00.