I had to go to three dictionaries before I found one that gave credence to my understanding of the distinction between "bitter" and "embittered", but at Cambridge's online dictionary, there is this definition:
embitter, v. to make someone feel angry and unhappy for a long time
So the difference between someone who is bitter and someone who is embittered is that the bitter person is bitter about some specific thing right now, while the embittered person is consistently bitter (and is likely to express their bitterness on a variety of matters), has probably been bitter for a long time, and shows no signs of relenting from their habitual bitterness.