The rose bush in this novel is another example of a symbol, just like the character of Hester Prynne, that defies easy interpretation and eschews classification. The narrator remains deliberately vague about how this important symbol can be interpreted, but what I think your question refers to is one possible legend that is cited as a potential explanation for the existence of the rose bush at the prison door, which is a rather incongruous place for a such a beautiful flower to grow. Note what the text tells us about this:
This rosebush, by a strange chance, has been kept alive in history; but whether it had merely survived out of the stern old wilderness, so long after the fall of the gigantic pines and oaks that orgiinally overshadowed it--or whether, as there is fair authority for believing, it had sprung up under the footsteps of the sainted Ann Hutchinson, as she entered the prison door--we shall not take upon us to determine.
Thus we can see that one potential story that explains the existence of the rose bush is that it sprang up beneath the saint Ann Hutchinson as she entered the prison door, but the truth of this rumour is never given.