The direct quote from the book is:
This rose-bush, 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 originally 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. Finding it so directly on the threshold of our narrative, which is now about to issue from that inauspicious portal, we could hardly do otherwise than pluck one of its flowers, and present it to the reader. It may serve, let us hope, to symbolise some sweet moral blossom that may be found along the track, or relieve the darkening close of a tale of human frailty and sorrow.
So, basically the rose bush is a symbol for people, that perhaps even in prison there is hope. The legend is that it sprang up because of the footsteps of the sainted Anne Hutchinson.