
Recently in New Avengers
LINK,
Jessica Drew re-told her origin story to Steve Rogers in order to explain why she appeared to be a double agent working for Hydra. Brian Michael Bendis must have liked telling that story so much that he wanted to do a deeper dive.
(I’m sure her busty appearances on the covers of New Avengers didn’t hurt, and they’re repeated here.)

Strong ties are drawn between Jessica Drew and Hydra Wundagore Mountain experiments. Miles Warren is revealed to be one of the scientists who helped create her, thus also strengthening her ties to the Spider-Man universe. We see that she was bombarded with experimental radiation while still in her mother’s womb, and her father was one of the scientists working on these Hydra projects.
In short, her childhood origin is pretty different here than both the one from her debut and from the recent New Avengers story. Rather than High Evolutionary being her creator, it’s all Hydra—but it still does take place on Wundagore. I like this because she’s not really consistent with High Ev’s work and because having a little bit of truth in the lie (i.e., that she was raised on Wundagore) makes the Hydra brainwashing that much more plausible. Oddly, although this is a much better origin story, later creators ignored the elements that differed from the previous origin story. I’m not sure it’s all canon.
The differences are explained as Mentallo having created in her mind memories of Bova, High Evolutionary, etc.

She then grows up a Hydra kid, gets trained by Taskmaster , is assigned to infiltrate SHIELD, rescue a Hydra agent (who is also her boyfriend), and kill Nick Fury…These parts are pretty consistent with prior tellings. We get more details, though, and they’re good. When she fails to kill Fury and is captured by SHIELD, we see her witness Hydra committing terrorist acts and realizes she’s been raised to believe in lies. She also sees how they really treated her—keeping her in a coma for ten years to continue experimenting on her, e.g., which is new information for us readers.
Fury turns Drew good, in part, by promising to help find her parents. She is too late to be reunited with her mother, who is killed by Hydra before Jessica can get to her. She’s actually killed by Whiplash, who was hired by Hydra.

She then sleeps with a Hydra scientist for information about where to find her dad—showing how far Jessica is willing to go to avenge her mother. Her father is still a Hydra scientist but he, too, is killed as a result of Jessica trying to get to him.
In the aftermath, she decides to become a private eye, separating herself from SHIELD and Hydra alike–that’s how we get to the first issue of the original Spider-Woman series. We do get a final page promising another solo book next year.

Note that the art for this miniseries is done by the Luna brothers. Together, they’ve done some remarkable indie work including Ultra, Girls, The Sword and Alex + Ada. Highly recommend you go find them and read ’em. All of ’em!
Fans seemed not to respond to this series because it’s not consistent with other Spider-Woman lore, but there are lots of modern origin stories you could say that about. Batman: Year One. Punisher: Born. Multiple Iron Man origin adjustments. It doesn’t make the comic bad if it tweaks known conventions. If all Marvel did was re-tell what you already read they would have become boring after ten years of storytelling.