You'll know the end of the Kyoto- Hachiman- Kizu bikepath by this large sign for the Kizu River, which you've been following for some time now. To continue on in the same direction (toward Nara), you have to turn RIGHT here... though you wouldn't know it since there's no sign telling you that there's another bikepath nearby. The road is local route 24, and it can get a bit clogged with cars. You'll only have to be on it for a couple of kilometers, though.

Here is the view to the right of the picture above - the blue sign says "Bikepath End" and shows the highway (route 24). And another of the bikepath route maps shows the entire route.