Takayama to Mt Fuji travel

Hi, planning to travel from Takayama to Mt Fuji.
The plan for now.

Takayama → Nagoya (Hida express Train) → Mishima (Shinkansen) → Kawaguchiko (Bus)

Have also heard that there is a Limon Bus that goes directly from Takayama to Kawaguchiko. But I am not able to find much details on how reliable this information is.

Any guidance or experiences, please do share! Thanks.

by Healthy-Body-8607