How to visit Shirakawa then Mt. Fiji

I will be visiting Japan next July to climb Mt. Fiji. My flight is via Tokyo. Can I go Shirakawa first then Mt. Fiji? And how? Your kind assistance will be much appreciated. Thank you.

Yes, there are quite few different ways of travel:

Option 1) take the bus from Shirakawago to Nagoya (or train and bus via Takayama), then the Shinkansen to the base of Mount Fuji. (probably the fastest, especially in case you climb from the Fujinomiya 5th Station)

Option 2) take the bus from Shirakawago to Kanazawa, then the shinkansen to Tokyo and then the bus to the 5th Station. (comfortable but expensive)

Option 3) take buses from Shirakawago via Takayama to Matsumoto, then a train to Kofu and then buses via Kawaguchiko to the 5th Station (complicated but cheapest)

http://www.japan-guide.com/e/e5953.html