Access by Bus to Fujiten snow resort from Kawaguchiko

Unfortunately no.
Its a great resort, the problem with this place is transportation. There is no shuttle bus nor other mode to come to this resort but by hiring a taxi from Kawaguchiko St.
The price isn't high though. 4,500 Yen for about 20 minutes. Although some people reportthey paid 6000 yen, so bring an extra 1500 just in case.

If you get an international drivers license before you leave your country, you could rent a car just outside Kawaguchiko Station or nearby. It would probably be around 7000 yen for the whole day and you wouldn't have to wait for taxis. Also, getting to Fuji-ten is very easy, it is just a left hand turn off route 139 when you see the Fuji Ten signs.
http://www.nipponrentacar.co.jp/service/ryokin1es.htm

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Actually I just found some information for a bus tour in the japanese website of Fujiten
http://www.fujiten.net/pc/bustour/index.shtml

Please take a look at this PDF:
http://www.fujiten.net/pc/bustour/kawaguchiko_bustour.pdf
What I recommend is calling them. maybe you can find someone who can speak japanese and call for you to get information.

I'm posting a translation below, I know its difficult to understand, but its just to help:

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Bus tour
Great deals
Period January 5 - February 28, 2018
2,500 yen (tax included)
[Organizer]
Yamanashi Prefectural Governor Registration Travel Business No. 2-230
Travel Department, Fujimi Kohden Development Co., Ltd.
Comprehensive travel business handling manager Nobunaga Sawanoh
【Inquiries】
Fujishima Koho Development Co., Ltd. Department of Transportation Travel Department
TEL 0555-73-1391
Tour NO FT-2210
Bus tour super deals
Period January 5 - February 28, 2018
2,500 yen (tax included)
Kawaguchiko station - roundtrip bus fare between the station
Reception is at Kawaguchiko Station front
Fujisaki Hikari Development Co., Ltd. Head office 1st floor
(We will begin acceptance 30 minutes before departure time.)
It takes about 20 to 30 minutes by car from Kawaguchiko Station - Futosan Snow Resort.
Ease
This building!
Bus Stop
Kawaguchiko Station
Bus Stop
seven
Eleven Bank
Bank
Our company
Lake Kawaguchiko
Souvenir shop
Kawaguchiko Station
Fujiyoshida
Common
Coupon tickets can be used for restaurants, souvenirs, lift tickets purchase and rental!
rotary
A slope
A bus written FT-2210 is a landmark
FAX 0555-72-5591
In front of the center house
Center house
We can not accept any time change after ticketing.
Accepting reception on the day OK!
Let's go!
(+ 1,000 yen coupon ticket that can be used on the set is set)
From Kawaguchiko station
From emergency
Kawaguchiko station - roundtrip bus fare between the station
time table
9: 30 10: 45 13: 30 15: 30
10: 00 11: 30 15: 00 16: 30
Sunrise Tour of Fujishima Hikari Development

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I hope it helps you!