Spider-Woman's history is exactly the same as that of Earth-616's Hummingbird up until the Marvel NEW! relaunch.
After seeing all the good Julia Carpenter did, she changed the way she looks at her powers. She decided to use them more spider-like and adopted the name of Spider-Woman. She began to use her psionic powers towards big threats. When the Avengers were formed she asked to be a part of it and demonstrated her new powers to them. They agreed and she has so far failed to disappoint.
She has the same powers as she did before, except more advanced in the psionic fields.
* Psionic Powers
** Wall Crawling
** Pychokinetic Webbing
* Telepathy
* Astral Projection