You can take a regular local bus(路線バス), non-reserved, only 3 in a day.http://www.shibazakura.jp/liner/
About 5 min short ride fr Motosuko(本栖湖) or 7 min fr Motosuko-iriguchi(本栖湖入口) bus stop.
(Fes web bus timetable is simple, major stops only.)
But couldn't find which "Motosuko bus stop" using, at lake side here or other side. https://goo.gl/maps/vs27FqQyxGG2https://goo.gl/maps/wWDb2fzoBdE2
Anyway, find "For Shin-Fuji stn.(新富士駅 行き)" bus timetable, ASAP.https://i.imgur.com/SeIA6mT.jpg
Motosuko-iriguchi bus stop is fixed, no problem.https://goo.gl/maps/xA4KGXbpQS52
Also couldn't find bus fare, bc fes place stop is not regular, no listed.
But maybe 330Y or a bit cheaper/oneway adult.
Also you can ask at Lake Motosu Tourism Association office.
(本栖湖観光案内所 Motosuko kankou an-nai-jo/sho)https://goo.gl/maps/nhRgLdP9DCP2https://goo.gl/maps/hf9TND1iAgqhttp://www.fujisan.ne.jp.e.aca.hp.transer.com/link/tel_book.php
(this "ko" means just "lake", Motosu"-ko" and last "jo/sho" are not long tone)
There seems to be a rental cycle, but no cheap, no recommended it.http://www.fujisan.ne.jp/view/info.php?no=855
Although, the route is simple and about 30 min ride maybe not so hard,https://goo.gl/maps/QznZC8ha5Qv
but don't know "where to go?" after fes site out.
If I were you, many tourists coming by own or rent a car to Lake Motosu,
so it will be faster "hitchhike" at car park than waiting for a limited bus.