Direct bus to Mt Fuji 5th station?

I'm planning on climbing Mt Fuji on Thursday 6th July using the Yoshida Trail. From what I've researched so far I understand that there's a bus from Shinjuku to Mt Fuji 5th Station (Fuji Subaru Line) but after looking at the highway bus website it says that there isn't a direct bus at the time of year I'm planning on going. Is this correct? It does give an alternative to this route (Shinjuku to Kawaguchiko and then onto Mt Fuji 5th Station) and I was wondering how convenient this is? Is it well sign posted at Kawaguchiko station? How often do those buses run? And do I need to make a reservation from Kawaguchiko to 5th station? Thanks in advance :)

The service information for the Shinjuku-5th station line for this summer (from 1 July) has not been announced yet; wait some more.

The official but time table between Shinjuku and Mt Fuji 5th sta will be released Mid or Late June each year.

Thank you :) I'll check back in a few weeks!