The Odakyu Fuji Hakone Pass includes a round trip between Shinjuku and Kawaguchiko, where you have to take the highway bus one way and take the train in the other direction. Therefore if you have a valid Fuji Hakone Pass, and make an online reservation in advance for the bus, you will not have to pay.
BE AWARE OF: Passes purchased at Odawara Station do not cover the train trip between Tokyo and Hakone and the highway bus ride between Tokyo and the Fuji Five Lakes.
Also it is not possible to get off at stations between your departure station and the free area.
Hope this can help you and have nice trip!