I've done some training using a murse/jack bauer bag, and it was not fast.
Have you ever seen or handled a womens' purse specifically designed for carrying a handgun?
Mrs. Submareener sees no need to draw to shoot from her purse. The store said they would give her a new one if she ever had to shoot through it. For revolvers only, of course!
My wife uses a fanny pack. It’s a compromise. Not as easy to snatch as a purse, and access to the piece is virtually instantaneous, due to the pull-away velcro container.
I use an inside-the-pocket holster with a small .380 (ppk/s).