Yes, there are direct buses operated from Shinjuku to the venue during 14th April to 27th May ( it may changed depends on the condition of Shibazakura).
Please check the timetable from the link below;
If you want to take this bus then you need to book in advance.
And also there are some buses from Kawaguchiko station operated.
This bus is called "Shibazakura Liner " and just a local operated bus so you don't need booking in advance.
Please just wait at the bus stop.
There are so many people to get the bus so you will have to queue on the line but the bus company will operate extra buses depend on the situation.
So you don't have to worry that much to take long to get on the bus.
Timetable is from the link below;
And Arakurayama Sengen Shrine is at the opposite of the venue, Kawaguchiko station is on the half way.
So I suggest you to get back to Kawaguchiko station and take a taxi.
Or you can take a train from Kawaguchiko station to Shimo-Yoshida station (approx 15 mis, 4 stations) then walk approx 10 mins.
You need to book in advance for the highway bus from Shinjuku to the venue, but you don't for the other transportation which I wrote above.
Hope this can be your help, and enjoy your trip in Japan!