Two things you should know about her that are important:
1.She can switch between aggro and zoning, but is mainly a zoning character.
2.Do not mash against King.
Starting with the first point, she is a zoning character and is very, very good at keeping you out as well as rushing you down. The first thing you need to do is always keep in mid to close range. As much as King is an unequipped character, her fireball is a very versatile move and can hurt a lot.
This is pretty basic, but you should try to hop a bit more. Aside from her EX Trapshoot, she's very vulnerable to air unless she's in the air. This is why being close to her is good. If she jumps, you can standing A her before she gets a fireball off. You want to constantly pressure her into making mistakes. You can punish practically anything she does at close range, none of her moves are safe, but at a distance and good spacing, she can cause a lot of problems. This solves your problem with d.B because if you apply hop pressure, you'll avoid her d.B all together.
My second point is not to mash against her. You have to take it slow because she does have reversals, namely her EX trapshoot. It is fast and will catch you if you hop at her, spam low kicks on her wake up or generally whiff a slow move near her. You want to take it slow. Make her make mistakes, tick throw, and what not. Remember that she can get a combo off from her st. D or d.B, but she has to combo her df+D in order to combo so always remember to block low. In arcade version, she can't cancel df+D by itself alone and blocking her whole string up close is good. Tornado kick is not safe on block if she is close up so punish it. A fast poke will get her if she does venom strike.
