In all of my unit testing, I've never bothered testing private functions. I typically just tested public functions. This goes along with the Black Box Testing methodology.
You are correct that you really can't test the private functions unless you expose the private class.
If your "seperate class for testing" is in the same assembly, you can choose to use internal instead of private. This exposes the internal methods to your code, but they methods will not be accessible to code not in your assembly.
EDIT: searching SO for this topic I came across this question. The most voted answer is similar to my response.
