What is the best way to go see Mt. Fuji at the end of October?

Hi, my husband and I are visiting Tokyo at the end of October. We really want to see Mt. Fuji if it's possible and want to know the best possible day trip itinerary. Are there buses that still go there at that time? Should we get the Mt. Fuji round trip tickets? Does the JR rail pass cover going from Tokyo to Mt. Fuji? What time should we head out? We would like to know the options.

If we can, we would like to step foot onto Mt. Fuji, literally just one foot is fine. We don't plan on hiking due to non-hiking season dangers. Basically, we want to say that we've been there/seen it and can take an awesome picture (if we are lucky to have clear skies).

I saw some day trip tours to Mt. Fuji/Hakone, but I'm not sure if it is worth the price ($130, we are trying not to overspend). Any help and suggestions is greatly appreciated.

Thanks!

Chris