Yes, there is a bus from Gora (the station close to the Owakudani) that goes to Gotemba outlet, then from there to Fujiyoshida, I think Kawaguchiko station.
When I did it in 2012, I used the 3 days Odakyu free pass, that icluded all the transport (train, bus, boat, ropway) in the area. If I remember correctly, the return to Tokyo from Fujiyshida was by bus.
However, on the Odakyu website, the pass seems to only include the Gotemba/Hakone part. Maybe it changed since I did it, so it might be an idea to ask at the Odakyu info desk in Shinjuku (where you can buy the pass) if there is still a version that goes up to Fujiyoshida.
Free Pass : http://www.odakyu.jp/english/deels/freepass/hakone/
Bus to and from fujiyoshida : https://www.city.fujiyoshida.yamanashi.jp/div/english/html/access.html
If you go before the end of March, there is a Doraemon stamp rally (stamp rally is the best thing in Japan) : http://www.odakyu.jp/release/nonbiri_2016/stamp/