Hike Mt. Fuji from Hakone

Hi guys,

me and some friends want to hike Mt. Fuji. In out itinerary it would make sense to do it before we go to Tokyo, so we thought about booking a hotel in Hakone, experiencing the Onsen there and then hike Mt. Fuji from there. We're planning on doing it on the 08th of July.

From what I read, Subashiri Trail makes the most sense, buuuut the buses from Gotemba Station to Subashiri 5th station only start operating on the 10th of July, I think. Is there any other way to get cheaply to the start of the trail?

On another note: Are we missing anything, do you see any easier or more recommended version of doing the hike when we're coming from the south and not from tokyo?