If you're trying to handle her more than a few times a week, there is a good chance she is just stressed from being disturbed so much. I take it these are defense bites (striking and letting go) and not feeding response bites (biting and holding on/constricting)? If they are feeding response bites, she may not be getting enough to eat.
Also, as state before, she could be about to shed, which usually causes snakes to become more easily agitated. Try to handle her less - if she has been biting "people" and not just you, she is most likely being handled too often. Try letting her rest for at least a day or two between being taken out of the cage.
Whoever her owner was during the past five years might have barely handled her at all, so she tolerated it more easily when it did happen. I rarely handle my snakes at all, only when necessary, and they are perfectly calm when I do.
Additionally, when you are actually handling the snake, don't be fearful of her (especially when you are getting her out of the enclosure). A nervous human hand jerks and flinches when in the tank, which to the snake looks and feels like a predator (which may trigger defensive behavior). Be calm, gentle, and confident when handling your kingsnake. If you're worried about her biting, I find that most people feel more confident when wearing long sleeves (like a sweathshirt) to "protect" themselves.
Hope that helps a bit.
-----
- Natalie
(San Francisco Bay Area)
1.0 Banded California King
1.0 Mexican Black King
1.0 Goini Kingsnake
1.0 Bay of LA Rosy Boa
2.1 Kenyan Sand Boas
1.2 Rubber Boas