You get an international driving permit from your home country:

http://en.wikipedia.org/wiki/International_Driving_Permit

No problem at all to rent motorcycles and cars with that. While
the convention says that you should have your original driving
license available I never have done that (could be lost) and I
have never been asked for that.

And seriously: If you are not in an English-speaking country, could
you tell if someone is showing you your original, home-country license and not your
health insurance card ? (No, the German license does not show anything
in English)

EDIT: Oops, I did not see that you have not the requirement for motorcycles,
I have not read it carefully enough. So strictly speaking legally *no, it is
not possible to drive a motorcycle with only an automobile license*.
If it is tolerated I do not know, perhaps someone from Bolivia or traveling
to it could answer that.

As I have a motorcycle license myself I am sorry to say that, but driving
a motorcycle in a third-world country if you have no road experience is
asking to get killed. You need to drive carefully even here because you
have to get the "sense" how people react because you have no protection
(the leather gear and helmet protects against falling down (sometimes
deliberately to save your life)) against collisions and stupid drivers.