Shibazakura Festival, Pink Moss Festival, is held at the northwest of Mount Fuji.
It takes more than 2 hours and 40 minutes away from Shinjuku. It takes 35 minutes at least from the closest railway station, Kawaguchiko Station. Route 139 is famous with traffic congestions.
http://www.shibazakura.jp/eng/access/
Maybe you will think the bullet train will save you time, but Bullet train is running South of Mount Fuji, very close to the seashore.
If you check the map of the above page, you can see the blue line showing the Shinkansen, the Bullet train. If you would try to get to a Shinkansen station from the area, check MISHIMA station. Don't forget the buses are not that frequent.