After thinking about it for a bit, I would re-write even the two sources to which I cited:
Anne clearly states that "It pleased God to keep me a long time without child." Since the first child is born ca. 1631-2, I would then make the marriage of Anne and Simon Bradstreet ca. 1627, giving her a 4-5 year time waiting for a child.
That puts her birth more in line with ca. 1606. This works. Thomas Dudley married on 25 April 1603. His eldest child, Thomas could be born ca. 1604, leaving a gap to 1608 for Anne. If born in ca. 1606, she is only 46 at the birth of her last child in 1652 (for which we do have a record). If it were me, I would now say ca. 1606-1672 as more likely.
P.S. She is not my director ancestor, but the sister-in-law of my ancestor's brother. My ancestor George Denison's brother Daniel married Anne's sister Patience Dudley.