Access to Gotemba Station from Kawaguchicko

I am planning to go from Shinjuku to Lake Kawaguchi and stay overnight to view MT Fuji on 18/11. Then will be going from Kawaguchiko Station to Hakone on 19/11/2014. From what I understand I have to go to Gotemba Station to take the Hakone Tozan Bus. May I know I can I get from Kawaguchiko Station to gotemba station by public transport and how long it would takes? Will the public transport operate on 19/11/2014 and where can I find the time schedule in English? Do you think it is better to both nights in Hakone? Would appreciate if you can help me with my questions? Thank you
Kim

- Hakone: Access and Orientation
http://www.japan-guide.com/e/e5206.html
The way from Hakone to Kawaguchiko is explained in this article. Basically you can do the reverse.

Time data of some Fujikyu Yamanashi buses:
07:10 / 08:10 / 08:50 / 09:30 / 10:10 / 10:50 .... Kawaguchiko Station (departure),
08:25 / 09:20 / 10:00 / 10:40 / 11:20 / 12:00 .... Gotemba Station (arrival).
- Source (in Japanese)
http://bus.fujikyu.co.jp/line/jikokuhyo/01.html

Dear Omotenanshi,

Thank you for your useful information on the bus schedule. Do you know whether they bus operates on 18/11 to 20/11? Does it operate daily?

Thank you