You have to understand how kings thermoregulate in the wild to envision how your tank should be setup.
In the "wild" kings basically use the earth as their method of absorbing heat when they need to and as a tool to escape heat. Believe it or not, they do make use of cooler temps than you might think for various reasons.
Typical scenario: sun warms the ground to a depth of a few inches, snake comes up a burrow close to the surface to get warm. Or maybe in and among tree roots, or brush.
Kings will make use of artificial cover (like plywood and metal signs) that gets warmed by the sun. Snake goes under cover, cover gets warmed by the sun and transfers warmth to snake.
So you can use a bulb if your cage provides the following:
1. A substrate like Eco Earth that can be deep enough for the snake to escape the heat by burrowing (kings love to burrow) and that can be kept slightly damp in areas to keep the snake hydrated.
2. A hide thingy, like a piece of plastic or plywood to hide under, etc.
3. You insulate the glass tank somewhat. I use corrugated plastic sign material cut to size with a straight-edge and knife, then tape some aquarium background to that, then mount to the outside back wall of the aquarium. This helps to keep more heat in. Also, cover some of the screen top.
Note on undertank heat:
It is usually easier to use heat pads for smaller snakes like most kings. Heat pads use less power, and do not dry out the air in the tank. Most people use heat pads for those reasons. You can't argue with success.