Does anyone know if there is a direct train from Kyoto to Hakone? I use hypermedia.com and the most direct requires 4 transfers through different trains.

using hyperdia you would have to check from Tokyo to Odawara(the Hakone JR station)

See here for further transport info to Hakone

http://www.japan-guide.com/e/e5206.html

Aloha!

I saw that there's a bullet train from tokyo direct to Hakone. I am trying to figure out if it's worth going from Kyoto straight to Hakone or go back to Tokyo and take the train from there.

On the Japan guide site I left above, just change the "Show Access Information" button to show "To/From Kyoto" and the info will come up.

The shinkansen goes direct from Kyoto to Odawara(Hakone). It will be one of the slower Kodama's or occasional quicker Hikare trains......no Nozomi

Aloha!

> I saw that there's a bullet train from tokyo direct to Hakone.

No bullet train direct to Hakone. Odawara is not Hakone.

sorry, did not see the "direct" part of the question.
Yes there is a direct train from Tokyo to Hakone but you cannot use your JR pass for it.

Odakyu Railways operates direct trains between Tokyo's Shinjuku Station and Hakone-Yumoto Station. The one way journey by the "Romance Car" limited express takes about 85 minutes and costs 2020 Yen. By slower express trains (kyuko), the journey takes about two hours, but costs only 1150 Yen.
This information is on the link I left for you earlier

Aloha!

The usual route from Kyoto to Hakone involves getting a Hikari Shinkansen (some stop at Odawara but most don't) to Shizuoka and change for slower Kodama to Odawara, or take a Hikari or faster Nozomi (JR Pass not valid) to Shin Yokohama (if your train stops there) or Shinagawa (all stop there) and backtrack to Odawara on Kodama (just one or two stops). You then change platforms and ride on retro-look Hakone Tozan rail car to Hakone.

I just answered this on the other thread. Additional info that I offered there is that there is a Hikari through train from Kyoto to Odawara approx every two hours.