This is a bit of a difficult one. In English, you'd pronounce it almost as though it were spelt "sowry" ie the "rr" is pronouced just like "wrap". But in Dutch, I think you sort of need to bring your tongue done from the roof of your mouth as you say it so that the "r" is almost rolled, and pronounce it a little bit more from the back of your throat. Does that make sense?
It has been my experience that the American English pronunciation of "sorry" has almost as many versions as there are American dialects.
Not to mention, that the word is often so loaded with context and/or emotion that it will be pronounced differently at different times by the very same person.
For example, the word is often stretched out slowly to clearly indicate that you are not sorry in the least.