Hello,
This is Hirokane at Local Travel Partners.
I hope you and your family are safe and fine.
Today, I would like to share “How to get to Mount Fuji (Yoshida Trail) by bullet train (Shinkansen)?”

To be precise, we can not reach Mount Fuji only using Shinkansen (bullet train).
Shinkansen + sightseeing shuttle bus is correct.
This is a recommended way for people who want to get to Mt.Fuji easily and stay at a luxury ryokan hotel and spa.
(2 nights at a ryokan and 1 night at a mountain hut)

The itinerary is below.
This is the itinerary that we arranged for our guest from Norway (photo below) in 2019.
Day 1,

1, Arrive at JR Mishima Station by bullet train (Shinkansen)
(It takes about 50 minutes from JR Tokyo Station)
2, Take a reserved shuttle bus which the Hotel Kaneyama-en (near the Lake Yamanaka)  provides. (It takes about 2.5 hours including one time stop for sightseeing)
3, The bus will stop at a sightseeing spot (spot changes with the season) and reach the hotel.
(This shuttle bus is served only for guests who will stay at Hotel Kaneyama-en.)
4, 1 night at the ryokan.  Great enjoyment!
Beautiful Japanese garden, Matcha service at their tatami room, delicious Japanese Kaiseki meal, Powerful Japanese drum (taiko) show by their staff every night, majestic Mt.Fuji view from the open air bath (hot spring spa)  and wearing kimono experience ( an option).

Japanese drum (taiko) show by the staff of the hotel (every night)

Day 2, 
1, Leave your luggage at the hotel and take a shuttle bus to Mt.Fuji station.
(Keeping luggage is served only for guests who will come back and stay at this hotel.)
2, Transfer to a Mt.Fuji climbing bus which will take you to the 5th Station of Mt.Fuji.
3, Get off the bus and start climbing.
4, Reach a mountain hut Hakuunso (the 8th Station of Mt.Fuji).
stay 1 night (dinner and bento breakfast will be served.)

Hakuunso, mountain hut / the 8th Station of Mt.Fuji

Day 3, 
1, Very early morning, Leave the mountain hut and head to the top.
2, Reach the top of Mount Fuji and view the sunrise called “Goraiko” in Japanese.
3, Enjoy the top and going down.
4, Reach the 5th Station, take a Mt.Fuji climbing bus to the Mt.Fuji Station.
5, Transfer to a taxi and go back to the Hotel Kaneyana-en, 1 night.
A relaxing time at an onsen and a delicious meal will refresh you after the hard work.

Day 4,
1, Check out, Take the reserved shuttle bus.
(This shuttle bus is served only for guests who stayed at Kaneyama-en.)
The bus will stop at a sightseeing spot and take you to the JR Mishima Station.
2, Head to the next destination from the JR Mishima Station

If you are interested in this arrangement, please feel free to contact us.
We are happy to arrange the whole itinerary.

We also look forward to welcoming you in Shizuoka, too.

When you plan Mt.Fuji climbing, please check the official website of Mt.Fuji.

We look forward to welcoming you after the pandemic is over.

Thank you!