Fujikyu Bus Mishima to Kawaguchiko

I am climbing Mt Fuji on Sunday 5 July, 2015 and staying in a mountain hut before completing climb on Monday 6 July 2015.
Travelling from Kyoto I want to catch bus from Mishima to Kawaguchiko.
Has the climbing season bus timetable commenced by that date?
Do I need to book Express bus ticket in advance? If so where do I book in Kyoto?

Travelling from Kyoto I want to catch bus from Mishima to Kawaguchiko.

Have you considered going via Shin-Fuji Station and climbing the Fujinomiya trail instead. Its a much more direct route to the summit. Otherwise you'll be travelling all the way around the mountain before you even start the climb.

Has the climbing season bus timetable commenced by that date?

Yes, the Kawaguchiko bus to the Fuji Subaru 5th Station and the Shin-Fuji bus to the Fujinomiya 5th Station both run from July 1st.

Do I need to book Express bus ticket in advance?

You don't have to book in advance, but it may be a good idea considering the 5th is a weekend. More info here:

http://www.japan-guide.com/bus/gotemba.html
http://www.japan-guide.com/bus/fuji_season.html