Clarifying usage and definition of 怀疑
First we will deal with the origin (English):  

doubt is, in a sense, questioning something
suspect is, on the other hands, distrusting something  

back to your example, you can identify the 2 sentences like this:  


  I doubt (this 100 yuan bill is fake)    


thus you are questioning the bill's..."fake-ness" which implies you think it's real  


  I suspect (this 100 yuan bill) is fake


thus you are distrusting this bill, thinking it's fake.

Now, to the translation:
我怀疑这张百元钞票是假的
is definitly the second explanation - I suspect this 100 yuan bill is fake.  

The way to express I doubt this 100 yuan bill is fake would be:
我对这张百元钞票是假的有怀疑

Hope this gives you an idea.