The route is as follows: take the train (back) to Tokyo station and use the Shinkansen from there to Osaka. Here is an example route. The route does take 360 Minutes, so bring something to do in the meantime. The 2nd route is to use a bus from Kawaguchiko to Mishima station and use the Shinkansen from there to Osaka.

The most efficient way to get from the Mt. Fuji area (specifically Kawaguchiko/Mt. Fuji Station) to Osaka is a two-step process. First, take a Fujikyuko Line train or a bus from Kawaguchiko to Mishima Station. The bus is often faster and more direct for this leg. From Mishima Station, you can catch the Tokaido Shinkansen (bullet train) directly to Shin-Osaka Station. The Shinkansen portion takes about 2 to 2.5 hours depending on whether you take the Hikari or Kodama train. Alternatively, you can take a train back toward Tokyo (Otsuki/Hachioji) and transfer there, but this is a significant backtrack. The total travel time is typically around 4 to 5 hours, and the cost is roughly ¥12,000 to ¥16,000. If you have a JR Pass, the Shinkansen portion is covered, but the private Fujikyuko Line from Kawaguchiko is usually an additional small fee.