Hi there,
The bus from Shinjuku to Mt. Fuji 5th station can be reserved from the following website as DiDi san mentioned.
http://highway-buses.jp/fuji/
However, the bus only operates from early May through the end of October, so there are no buses to go to Mt. Fuji 5th station on March 1st. If you would like to see Mt. Fuji, Kawaguchiko is the best place to enjoy the beautiful scenery of Mt. Fuji. The buses from Shinjuku to Kawaguchiko run throughout a year.
Have a nice trip in Japan!
Please share your experience of visiting Mt. Fuji and post some pics in March!