From IC Takaido to Katsunuma IC, it takes only 1 hour.
You can follow the route suggested here.
JR operates direct trains between Shinjuku Station and
Yamanashi City Station. The one way journey by Kaiji limited
express takes 1 hour and 30 minutes and costs \2,210.
Yamanashi City station is the sixth stop. For further information
about JR timetable see Hyperdia.
By Highway Express Bus -about 2 hours and 15 minutes
Bus service is also offered from Shinjuku Highway Express Bus
Terminal (JR Shinjuku Station West Exit). From Shinjuku, take
the bus and get off in Katsunuma. There, take a taxi for
Katsunuma Budokyo Station (about 10 minutes). Then, at
Katsunuma Budokyo Station take the JR Chuo-honsen local
train and get off two stops after, in Yamanashi City Station
(one way trip fare is \190).
Bus fare changes according to the bus company and bus type.
The ticket can be reserved in advance or can be bought
directly at the Bus Terminal.
For further information about timetable and fares see
Japan Bus Web.